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Mathematics
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hxthanh
  • Member for 11 years, 6 months
  • Last seen more than a week ago
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17
How to prove $ \sum_{k=0}^n \frac{(-1)^{n+k}{n+k\choose n-k}}{2k+1}=\frac{-2\cos\left(\frac{2(n-1)\pi}{3}\right)}{2n+1}$
May 31, 2015
16
Proof of the identity $\sum_{k=0}^{\min[p,q]}{p\choose k}{q\choose k}{n+k\choose p+q}={n\choose p}{n\choose q}$
Jan 17, 2013
15
How to prove $ \sum_{k=0}^n \frac{(-1)^{n+k}{n+k\choose n-k}}{2k+1}=\frac{-2\cos\left(\frac{2(n-1)\pi}{3}\right)}{2n+1}$
Jun 3, 2015
14
How to sum:$\sum_{k=1}^{n}(k²-k)$ without using this: $\sum_{k=1}^{n}(k²)=\frac{n(n+1)(2n+1)}{6}$?
Jun 9, 2015
10
Compare $\sum_{k=1}^n \left\lfloor \frac{k}{\varphi}\right\rfloor$ ...
Apr 30, 2015
9
Closed form for the sum $\sum_{k=0}^n a^k \left\lfloor\frac{k}{p}\right\rfloor$
Jun 8, 2015
6
How to closed the sum $\displaystyle \sum_{k=0}^n \dfrac{(-1)^k(2k+1)!!}{(n-k)!k!(k+1)!}$
Apr 12, 2014
6
Stars and bars (combinatorics) with multiple bounds
Apr 20, 2014
5
Alternating sum of reciprocals of binomial coefficients
Mar 1
5
Summation of product of $m+1$ alternate numbers
Jun 15, 2015