Evaluate $\sum_{k=0}^{n} {3n \choose 3k}$
72639
Show that $\sum_{k=0}^n\binom{3n}{3k}=\frac{8^n+2(-1)^n}{3}$
89576
Proof of a binomial identity $\sum_{k=0}^n {n \choose k}^{\!2} = {2n \choose n}.$
7083
Alternating sum of binomial coefficients: given $n \in \mathbb N$, prove $\sum^n_{k=0}(-1)^k {n \choose k} = 0$
4991
Proving by induction that $ \sum_{k=0}^n{n \choose k} = 2^n$
134311
How to determine equation for $\sum_{k=1}^n k^3$
81589
Find the sum of $\sum_{k=0}^{\infty} 1/[(r+2k+2)(s+2k+2)]$
14197
show that $\sum_{i=0}^l \dfrac{{l\choose i}}{{n\choose k + i}} = \dfrac{n+1}{(n-l+1) {n-l\choose k}}$
151375
There are $3$ Zero-Sum Numbers!
115433
Find the summation of given expression: $\sum_{k=1}^n k^3\binom nk$
87479
Closed form for $\sum_{k=0}^{n-p}\binom{n}{k}\binom{n}{p+k}$
90519
Combinatorial proof of $\sum\limits_{k=0}^n {n \choose k}3^k=4^n$
140877
Evaluate the sum $\sum_{k=1}^n {n \choose k-1} {n \choose k}$
128200
Sequence sum question: $\sum_{n=0}^{\infty}nk^n$
48200
Simplify $\sum_{i=0}^n (i+1)\binom ni$
68080
Evaluation of $\sum_{k=0}^n{n\choose k}^2u^k$
13236
Proving equality - a sum including binomial coefficient $\sum_{k=1}^{n}k{n \choose k}2^{n-k}=n3^{n-1}$
155496
sum of combinations $\binom n{0} + \binom n{3} + \binom n{6} +... +\binom n{3k}$