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\(2^n = \sum_{k=0}^{k=n} \frac{n!}{k!(n-k)!}\)

Note by Jack Han 2 years, 8 months ago

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2 \times 3

2^{34}

a_{i-1}

\frac{2}{3}

\sqrt{2}

\sum_{i=1}^3

\sin \theta

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Hint: What is the binomial expansion of \((1+x)^n \)? What happens when \(x=1\)?

Alternatively you can prove this via induction. Use the properties of Pascal Identity: \( \dbinom{n-1}{k-1} + \dbinom{n-1}k = \dbinom nk \).

Or see this: Binomial Theorem - N Choose K.

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Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

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TopNewestHint: What is the binomial expansion of \((1+x)^n \)? What happens when \(x=1\)?Alternatively you can prove this via induction. Use the properties of Pascal Identity: \( \dbinom{n-1}{k-1} + \dbinom{n-1}k = \dbinom nk \).

Or see this: Binomial Theorem - N Choose K.

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