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

Note by Bakshinder Singh 4 years, 1 month ago

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What's \(C_i\)? \(i\)-th Catalan number? – Zi Song Yeoh · 4 years, 1 month ago

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@Zi Song Yeoh – \(C_{i}^{2i}\) denotes combinations. – Bakshinder Singh · 4 years, 1 month ago

@Bakshinder Singh – I thought it was i-th Catalan number to the power of 2i. :) – Zi Song Yeoh · 4 years, 1 month ago

@Bakshinder Singh – same as \({2i \choose i}\) – Bakshinder Singh · 4 years, 1 month ago

expand it as (iC0)^2 + (iC1)^2 +........ (iCi)^2 and then summate each term separately.... – Jatin Yadav · 4 years, 1 month ago

Link – Harshit Kapur · 4 years, 1 month ago

@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, 1 month ago

@Bakshinder Singh – i know, but it is good to know that theorum too :) – Harshit Kapur · 4 years, 1 month ago

@Harshit Kapur – The summation still looks ugly after using it. Anyway it is a good theorem to know about. – Yong See Foo · 4 years, 1 month ago

It cant be solved by coefficent method approach. I tried!!! – Bakshinder Singh · 4 years, 1 month ago

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## Comments

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TopNewestWhat's \(C_i\)? \(i\)-th Catalan number? – Zi Song Yeoh · 4 years, 1 month ago

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– Bakshinder Singh · 4 years, 1 month ago

\(C_{i}^{2i}\) denotes combinations.Log in to reply

– Zi Song Yeoh · 4 years, 1 month ago

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

– Bakshinder Singh · 4 years, 1 month ago

same as \({2i \choose i}\)Log in to reply

expand it as (iC0)^2 + (iC1)^2 +........ (iCi)^2 and then summate each term separately.... – Jatin Yadav · 4 years, 1 month ago

Log in to reply

Link – Harshit Kapur · 4 years, 1 month ago

Log in to reply

– Bakshinder Singh · 4 years, 1 month ago

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

– Harshit Kapur · 4 years, 1 month ago

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

– Yong See Foo · 4 years, 1 month ago

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!!! – Bakshinder Singh · 4 years, 1 month ago

Log in to reply