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Add new skill for custom markdown to html covnersion
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# Writing Mathematical Expressions to HTML
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## Writing Inline Expressions
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### Markdown
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```markdown
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This sentence uses `$` delimiters to show math inline: $\sqrt{3x-1}+(1+x)^2$
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```
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### Parsed HTML
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```html
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<p>This sentence uses <code>$</code> delimiters to show math inline:
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<math-renderer><math xmlns="http://www.w3.org/1998/Math/MathML">
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<msqrt>
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<mn>3</mn>
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<mi>x</mi>
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<mo>−</mo>
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<mn>1</mn>
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</msqrt>
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<mo>+</mo>
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<mo>(</mo>
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<mn>1</mn>
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<mo>+</mo>
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<mi>x</mi>
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<msup>
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<mo>)</mo>
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<mn>2</mn>
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</msup>
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</math>
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</math-renderer>
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</p>
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```
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### Markdown
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```markdown
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This sentence uses $\` and \`$ delimiters to show math inline: $`\sqrt{3x-1}+(1+x)^2`$
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```
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### Parsed HTML
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```html
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<p>This sentence uses
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<math-renderer>
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<math xmlns="http://www.w3.org/1998/Math/MathML">
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<mo>‘</mo>
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<mi>a</mi>
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<mi>n</mi>
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<mi>d</mi>
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<mo>‘</mo>
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</math>
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</math-renderer> delimiters to show math inline:
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<math-renderer>
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<math xmlns="http://www.w3.org/1998/Math/MathML">
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<msqrt>
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<mn>3</mn>
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<mi>x</mi>
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<mo>−</mo>
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<mn>1</mn>
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</msqrt>
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<mo>+</mo>
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<mo stretchy="false">(</mo>
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<mn>1</mn>
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<mo>+</mo>
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<mi>x</mi>
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<msup>
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<mo stretchy="false">)</mo>
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<mn>2</mn>
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</msup>
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</math>
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</math-renderer>
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</p>
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```
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---
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## Writing Expressions as Blocks
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### Markdown
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```markdown
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**The Cauchy-Schwarz Inequality**\
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$$\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)$$
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```
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### Parsed HTML
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```html
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<p>
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<strong>The Cauchy-Schwarz Inequality</strong><br>
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<math-renderer>
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<math xmlns="http://www.w3.org/1998/Math/MathML">
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<msup>
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<mrow>
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<mo>(</mo>
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<munderover>
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<mo>∑</mo>
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<mrow>
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<mi>k</mi>
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<mo>=</mo>
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<mn>1</mn>
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</mrow>
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<mi>n</mi>
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</munderover>
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<msub>
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<mi>a</mi>
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<mi>k</mi>
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</msub>
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<msub>
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<mi>b</mi>
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<mi>k</mi>
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</msub>
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<mo>)</mo>
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</mrow>
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<mn>2</mn>
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</msup>
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<mo>≤</mo>
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<mrow>
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<mo>(</mo>
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<munderover>
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<mo>∑</mo>
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<mrow>
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<mi>k</mi>
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<mo>=</mo>
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<mn>1</mn>
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</mrow>
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<mi>n</mi>
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</munderover>
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<msubsup>
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<mi>a</mi>
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<mi>k</mi>
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<mn>2</mn>
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</msubsup>
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<mo>)</mo>
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</mrow>
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<mrow>
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<mo>(</mo>
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<munderover>
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<mo>∑</mo>
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<mrow>
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<mi>k</mi>
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<mo>=</mo>
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<mn>1</mn>
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</mrow>
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<mi>n</mi>
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</munderover>
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<msubsup>
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<mi>b</mi>
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<mi>k</mi>
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<mn>2</mn>
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</msubsup>
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<mo>)</mo>
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</mrow>
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</math>
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</math-renderer>
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</p>
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```
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### Markdown
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```markdown
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**The Cauchy-Schwarz Inequality**
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```math
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\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)
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```
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```
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### Parsed HTML
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```html
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<p><strong>The Cauchy-Schwarz Inequality</strong></p>
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<math-renderer>
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<math xmlns="http://www.w3.org/1998/Math/MathML">
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<msup>
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<mrow>
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<mo>(</mo>
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<munderover>
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<mo>∑</mo>
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<mrow>
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<mi>k</mi>
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<mo>=</mo>
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<mn>1</mn>
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</mrow>
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<mi>n</mi>
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</munderover>
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<msub>
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<mi>a</mi>
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<mi>k</mi>
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</msub>
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<msub>
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<mi>b</mi>
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<mi>k</mi>
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</msub>
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<mo>)</mo>
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</mrow>
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<mn>2</mn>
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</msup>
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<mo>≤</mo>
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<mrow>
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<mo>(</mo>
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<munderover>
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<mo>∑</mo>
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<mrow>
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<mi>k</mi>
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<mo>=</mo>
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<mn>1</mn>
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</mrow>
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<mi>n</mi>
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</munderover>
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<msubsup>
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<mi>a</mi>
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<mi>k</mi>
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<mn>2</mn>
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</msubsup>
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<mo>)</mo>
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</mrow>
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<mrow>
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<mo>(</mo>
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<munderover>
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<mo>∑</mo>
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<mrow>
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<mi>k</mi>
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<mo>=</mo>
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<mn>1</mn>
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</mrow>
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<mi>n</mi>
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</munderover>
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<msubsup>
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<mi>b</mi>
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<mi>k</mi>
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<mn>2</mn>
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</msubsup>
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<mo>)</mo>
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</mrow>
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</math>
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</math-renderer>
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```
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### Markdwon
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```markdown
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The equation $a^2 + b^2 = c^2$ is the Pythagorean theorem.
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```
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### Parsed HTML
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```html
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<p>The equation
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<math-renderer><math xmlns="http://www.w3.org/1998/Math/MathML">
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<msup>
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<mi>a</mi>
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<mn>2</mn>
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</msup>
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<mo>+</mo>
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<msup>
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<mi>b</mi>
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<mn>2</mn>
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</msup>
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<mo>=</mo>
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<msup>
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<mi>c</mi>
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<mn>2</mn>
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</msup>
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</math></math-renderer> is the Pythagorean theorem.
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</p>
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```
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### Markdown
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```
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$$
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\int_0^\infty e^{-x} dx = 1
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$$
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```
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### Parsed HTML
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```html
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<p><math-renderer><math xmlns="http://www.w3.org/1998/Math/MathML">
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<msubsup>
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<mo>∫</mo>
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<mn>0</mn>
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<mi>∞</mi>
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</msubsup>
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<msup>
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<mi>e</mi>
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<mrow>
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<mo>−</mo>
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<mi>x</mi>
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</mrow>
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</msup>
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<mi>d</mi>
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<mi>x</mi>
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<mo>=</mo>
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<mn>1</mn>
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</math></math-renderer></p>
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```
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---
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## Dollar Sign Inline with Mathematical Expression
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### Markdown
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```markdown
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This expression uses `\$` to display a dollar sign: $`\sqrt{\$4}`$
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```
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### Parsed HTML
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```html
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<p>This expression uses
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<code>\$</code> to display a dollar sign:
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<math-renderer>
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<math xmlns="http://www.w3.org/1998/Math/MathML">
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<msqrt>
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<mi>$</mi>
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<mn>4</mn>
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</msqrt>
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</math>
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</math-renderer>
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</p>
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```
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### Markdown
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```markdown
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To split <span>$</span>100 in half, we calculate $100/2$
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```
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### Parsed HTML
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```html
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<p>To split
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<span>$</span>100 in half, we calculate
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<math-renderer>
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<math xmlns="http://www.w3.org/1998/Math/MathML">
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<mn>100</mn>
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<mrow data-mjx-texclass="ORD">
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<mo>/</mo>
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</mrow>
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<mn>2</mn>
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</math>
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</math-renderer>
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</p>
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```
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