Evaluate $\sum_{k = 0}^{n} {n\choose k} k^m$
70248
Closed-form expression for $\sum_{k=0}^n\binom{n}kk^p$ for integers $n,\,p$
87479
Closed form for $\sum_{k=0}^{n-p}\binom{n}{k}\binom{n}{p+k}$
97007
Does $\sum_{m=0}^{\infty} {2m\choose m} \frac{1}{4^{m}} $ converge?
40784
$\sum_{k=m}^{n}(-1)^k\binom{n}{k}\binom{k}{m}=0, n>m\geq 0$
14239
How to show $\sum_{k=0}^{n}\binom{n+k}{k}\frac{1}{2^k}=2^{n}$
104704
Evaluate $\sum\limits_{k=0}^n \binom{n}{k}$ combinatorially
37148
How to evaluate $ \lim \limits_{n\to \infty} \sum \limits_ {k=1}^n \frac{k^n}{n^n}$?
68080
Evaluation of $\sum_{k=0}^n{n\choose k}^2u^k$
4991
Proving by induction that $ \sum_{k=0}^n{n \choose k} = 2^n$
82742
Proving that ${x +y+n- 1 \choose n}= \sum_{k=0}^n{x+n-k-1 \choose n-k}{y+k-1 \choose k} $
138542
Evaluating sums question $\sum_{k=2}^n \frac{1}{k^2-1}$
6838
Evaluate the series $S_n = \sum_{k=1}^n\log\frac {k (k + 2)}{(k + 1)^2}$
87589
Evaluate $\binom{n}{0}+\binom{n}{2}+\binom{n}{4}+...+\binom{n}{2k}$
39909
Getting a closed form from $\sum_{i=1}^{n-1} \sum_{j=i+1}^{n} \sum_{k=1}^{j} 1$
35381
Sum with binomial coefficients: $\sum_{k=1}^m  \frac{1}{k}{m \choose k} $
130083
Evaluating sum of a combination series
93813
How to show that $\sum\limits_{k=0}^n (-1)^k\tfrac{{ {n}\choose{k}}}{{ {x+k}\choose{k}}} = \frac{x}{x+n}$