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

Note by Bakshinder Singh
4 years, 3 months ago

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What's \(C_i\)? \(i\)-th Catalan number? Zi Song Yeoh · 4 years, 3 months ago

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@Zi Song Yeoh \(C_{i}^{2i}\) denotes combinations. Bakshinder Singh · 4 years, 3 months ago

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@Bakshinder Singh I thought it was i-th Catalan number to the power of 2i. :) Zi Song Yeoh · 4 years, 3 months ago

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@Bakshinder Singh same as \({2i \choose i}\) Bakshinder Singh · 4 years, 3 months ago

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expand it as (iC0)^2 + (iC1)^2 +........ (iCi)^2 and then summate each term separately.... Jatin Yadav · 4 years, 3 months ago

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Link Harshit Kapur · 4 years, 3 months ago

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@Harshit Kapur Sorry, I didn't got your point! Here n=i and you can't take n as constant in summation. Bakshinder Singh · 4 years, 3 months ago

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@Bakshinder Singh i know, but it is good to know that theorum too :) Harshit Kapur · 4 years, 3 months ago

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@Harshit Kapur The summation still looks ugly after using it. Anyway it is a good theorem to know about. Yong See Foo · 4 years, 3 months ago

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It cant be solved by coefficent method approach. I tried!!! Bakshinder Singh · 4 years, 3 months ago

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