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

Note by Bakshinder Singh 4 years, 8 months ago

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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....

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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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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.

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

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

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

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