Prove $\sum_{i=0}^{2n}{(-1)^i \binom{2n}{i}^3} = (-1)^n \frac{(3n)!}{(n!)^3}$
56138
Proving $\sum_{k=0}^{2m}(-1)^k{\binom{2m}{k}}^3=(-1)^m\binom{2m}{m}\binom{3m}{m}$ (Dixon's identity)
99249
Sum of product of binomial coefficients: $\sum_{k=0}^{n}(-1)^k\binom{n}{k}\binom{n + k}{k} = (-1)^n$
14239
How to show $\sum_{k=0}^{n}\binom{n+k}{k}\frac{1}{2^k}=2^{n}$
46840
How to prove that $\sum_{r=0}^n\binom{n}{r}2^r=3^n$
145019
Prove that $\sum_{n=0}^\infty \frac{(-1)^n}{3n+1} = \frac{\pi}{3\sqrt{3}}+\frac{\log 2}{3}$
49052
Find $\sum_{n=1}^\infty \frac{n^3}{n!}$.
153231
Why does $\sum_1^\infty \frac1{n^3}=\frac52\sum_1^\infty\frac{(-1)^{n-1}}{n^3\binom{2n}{n}}$?
126312
How can you prove $\binom {2n}{2} = 2\binom{n}{2} + n^2$?
49066
Give the combinatorial proof of the identity $\sum\limits_{i=0}^{n} \binom{k-1+i}{k-1} = \binom{n+k}{k}$
94580
Prove that, $\binom{3n}{r}=\binom{3n-1}{r} + \binom{3n-1}{r-1}$
1258
Prove $3^n = \sum_{k=0}^n \binom {n} {k} 2^k$
136580
Proving $\sum_{k=0}^n\binom{2n}{2k} = 2^{2n-1}$
111098
Prove $2^{2n} = \sum_{k=0}^{n}\binom{2n+1}{k}$
72026
Induction proof of $\sum_{k=1}^{n} \binom n k = 2^n -1 $
50226
Prove the identity $\sum_{k=0}^{n}\sum_{r=0}^{k} \binom{k}{r} \binom{n}{k} = 3^n$
5332
Find the value of $\sum_0^n \binom{n}{k} (-1)^k \frac{1}{k+1}$
40784
$\sum_{k=m}^{n}(-1)^k\binom{n}{k}\binom{k}{m}=0, n>m\geq 0$