# How will you solve?

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

Note by Bakshinder Singh
6 years, 2 months ago

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What's $$C_i$$? $$i$$-th Catalan number?

- 6 years, 2 months ago

$$C_{i}^{2i}$$ denotes combinations.

- 6 years, 2 months ago

same as $${2i \choose i}$$

- 6 years, 2 months ago

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

- 6 years, 2 months ago

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

- 6 years, 2 months ago

- 6 years, 2 months ago

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

- 6 years, 2 months ago

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

- 6 years, 2 months ago

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

- 6 years, 2 months ago

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

- 6 years, 2 months ago