Evaluating $\sum^n_{k=0}{n\choose{k}}{m\choose{k}}$ for fixed $m,n$
30472
Evaluate $\sum_{k=0}^{n} {n \choose k}{m \choose k}$ for a given $n$ and $m$.
112374
Evaluate $ \binom{n}{0}+\binom{n}{2}+\binom{n}{4}+\cdots+\binom{n}{2k}+\cdots$
56365
Evaluate $\sum\limits_{k=1}^{n} \frac{k}{2^k}$
70248
Closed-form expression for $\sum_{k=0}^n\binom{n}kk^p$ for integers $n,\,p$
634
Closed form formula for $\sum\limits_{k=1}^n k^k$
40784
$\sum_{k=m}^{n}(-1)^k\binom{n}{k}\binom{k}{m}=0, n>m\geq 0$
69943
why is ${n+1\choose k} = {n\choose k} + {n\choose k-1}$?
89279
If $\sum a_n/k^n = 0$ for all $k$, then $a_n = 0$ for all $n$
129304
Alternative combinatorial proof for $\sum\limits_{r=0}^n\binom{n}{r}\binom{m+r}{n}=\sum\limits_{r=0}^n\binom{n}{r}\binom{m}{r}2^r$
32791
Proving this binomial identity $\sum_{k=0}^n {n+k \choose k} \frac{1}{2^{k}}= 2^{n}$
146762
Closed form for $\sum_{k=0}^{n} \binom{n}{k}\frac{(-1)^k}{(k+1)^2}$
87320
Proving identities like $\sum_{k=1}^nk{n\choose k}^2=n{2n-1\choose n}$ combinatorially
92784
Intuitive (combinatorial) proof of $2^n=\sum_{k=0}^n {n\choose k}$
130083
Evaluating sum of a combination series
63879
Prove that $\sum_{k=0}^r {m \choose k} {n \choose r-k} = {m+n \choose r}$
125712
Working with binomial coefficient $\sum_{k=0}^n (-1)^k \binom nk=0$
146651
Evaluting sum $\sum \limits_{n=0}^\infty\frac{n^k}{n!}$