Evaluate $\sum_{n=1}^N {n \choose k} $
8476
Proof of the Hockey-Stick Identity: $\sum\limits_{t=0}^n \binom tk = \binom{n+1}{k+1}$
143132
How to reverse the $n$ choose $k$ formula?
56365
Evaluate $\sum\limits_{k=1}^{n} \frac{k}{2^k}$
63879
Prove that $\sum_{k=0}^r {m \choose k} {n \choose r-k} = {m+n \choose r}$
48200
Simplify $\sum_{i=0}^n (i+1)\binom ni$
115420
Evaluate $\sum_{n=1}^{\infty} \frac{n}{n^4+n^2+1}$
151085
Simplify the sum $ \sum_{i=0}^{k}(-1)^i i \binom{n}{i} \binom{n}{k-i}$
151757
Simplify $\sum_{i=0}^{N/2}{N-i\choose i}$
6366
Combinatorial proof of summation of $\sum\limits_{k = 0}^n {n \choose k}^2= {2n \choose n}$
133905
Intuitive proof of $\sum_{k=1}^{n} \binom{n}{k} k^{k-1} (n-k)^{n-k} = n^n$
58428
Proving $\sum_{k=0}^{n} {k \choose a} {n-k \choose b} = {n+1\choose a+b+1}$
103840
Calculate $\sum_{k=1}^n k2^{n-k}$
138542
Evaluating sums question $\sum_{k=2}^n \frac{1}{k^2-1}$
634
Closed form formula for $\sum\limits_{k=1}^n k^k$
87589
Evaluate $\binom{n}{0}+\binom{n}{2}+\binom{n}{4}+...+\binom{n}{2k}$
89367
Calculate $ S =\sum_{k=1}^n\frac {1}{k(k+1)(k+2)}. $
87479
Closed form for $\sum_{k=0}^{n-p}\binom{n}{k}\binom{n}{p+k}$