How will you solve?

Evaluate i=130Ci2i\sum_{i=1}^{30} C_{i}^{2i}

Note by Bakshinder Singh
8 years, 4 months ago

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3 votes

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Comments

What's CiC_i? ii-th Catalan number?

Zi Song Yeoh - 8 years, 4 months ago

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Ci2iC_{i}^{2i} denotes combinations.

Bakshinder Singh - 8 years, 4 months ago

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

Bakshinder Singh - 8 years, 4 months ago

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

Zi Song Yeoh - 8 years, 4 months ago

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

Bakshinder Singh - 8 years, 4 months ago

Link

Harshit Kapur - 8 years, 4 months ago

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

Bakshinder Singh - 8 years, 4 months ago

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

Harshit Kapur - 8 years, 4 months ago

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

Yong See Foo - 8 years, 4 months ago

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

Jatin Yadav - 8 years, 3 months ago
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