Question: Can anyone help to find closed form of following summation: $\sum_{i=0}^{20}(-1)^i\times\binom{n}{i}\times \binom{n}{n-i}$ ?
I think this problem have a raltion with $\sum_{i=0}^{20}(-1)^i\times\binom{n}{i}$ ,but i can't prove this claim.
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So,give me a hint to solve this problem.thanks – tstt Jan 17 '21 at 12:46
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1Note that $n$ choose $i$ is the same as $n$ choose $(n-i)$. – Tom Sharpe Jan 17 '21 at 12:46
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2$n=20 $ or not? Can you try smaller $n$'s and see if you can find a pattern? – Neat Math Jan 17 '21 at 12:48
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n most be $\geq 20$ – tstt Jan 17 '21 at 12:54