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Evaluate \(\sum_{i=1}^{30} C_{i}^{2i}\)

Note by Bakshinder Singh 5 years, 2 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

\boxed{123}

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What's \(C_i\)? \(i\)-th Catalan number?

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\(C_{i}^{2i}\) denotes combinations.

I thought it was i-th Catalan number to the power of 2i. :)

same as \({2i \choose i}\)

expand it as (iC0)^2 + (iC1)^2 +........ (iCi)^2 and then summate each term separately....

Link

Sorry, I didn't got your point! Here n=i and you can't take n as constant in summation.

i know, but it is good to know that theorum too :)

The summation still looks ugly after using it. Anyway it is a good theorem to know about.

It cant be solved by coefficent method approach. I tried!!!

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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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TopNewestWhat's \(C_i\)? \(i\)-th Catalan number?

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\(C_{i}^{2i}\) denotes combinations.

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I thought it was i-th Catalan number to the power of 2i. :)

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same as \({2i \choose i}\)

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expand it as (iC0)^2 + (iC1)^2 +........ (iCi)^2 and then summate each term separately....

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Link

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Sorry, I didn't got your point! Here n=i and you can't take n as constant in summation.

Log in to reply

i know, but it is good to know that theorum too :)

Log in to reply

The summation still looks ugly after using it. Anyway it is a good theorem to know about.

Log in to reply

It cant be solved by coefficent method approach. I tried!!!

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