Evaluate $\sum\limits_{k=m}^n (-1)^k {n \choose k} {k \choose m}$
40784
$\sum_{k=m}^{n}(-1)^k\binom{n}{k}\binom{k}{m}=0, n>m\geq 0$
37650
Find $\sum_{m=0}^n\ (-1)^m m^n {n \choose m}$
129801
Finding a closed form for $\sum^{n}_{k=1} \frac{k}{(k+1)!} $
116722
Simplifying $\big(\sum_{i=0}^n\binom{k}{i}\binom{M-k}{n-i}\frac{k-i}{M-n}\big)/{\binom{M}{n}}$
93813
How to show that $\sum\limits_{k=0}^n (-1)^k\tfrac{{ {n}\choose{k}}}{{ {x+k}\choose{k}}} = \frac{x}{x+n}$
132984
$\sum\limits_{k=0}^{\frac{p-1}2}3^k\binom{p}{k}\equiv 2^p-1\pmod{p^2}$
108971
Finding the limit of $\sqrt[n]{{kn \choose n}}$
60104
Evaluate $\sum_{k=1}^\infty\frac{x^k}{k(k+1)}$
59253
Summing the power series $\sum\limits_{n=0}^\infty (-1)^n \frac{x^{2n+1}}{2n+1}\prod\limits_{k=1}^n\frac{2k-1}{2k} $
19868
Evaluate: $ \sum _ {k=1}^{n}{\frac{k}{n}\binom{n}{k}t^k(1-t)^{n-k}}$
98082
Another combinatorics problem: $\sum\limits_{k = 0}^n (-1)^k \binom{2n-k}k2^{2n-2k}=2n+1$
5054
Calculate $\sum\limits_{k=0}^{\infty}\frac{1}{{2k \choose k}}$
123675
Evaluate the following limit of finite sum
90519
Combinatorial proof of $\sum\limits_{k=0}^n {n \choose k}3^k=4^n$
120976
Proving $\sum_{k=0}^{n}k{n\choose k}^2 = n{2n-1 \choose n-1} $
146762
Closed form for $\sum_{k=0}^{n} \binom{n}{k}\frac{(-1)^k}{(k+1)^2}$
71797
Combinatorial argument for $\sum\limits_{k=i}^{n}\binom{n}{k}\binom{k}{i} = \binom{n}{i}2^{n-i}$