How to derive a generic formula for $\sum_{k=0}^n k^p$ for any $p$?
50050
A formula for the power sums: $1^n+2^n+\dotsc +k^n=\,$?
96945
General formula of $\sum_{n\ge1}{\binom{2n}{n}^{-k}}$.
91933
Evaluate $\sum_{k=1}^nk\cdot k!$
104704
Evaluate $\sum\limits_{k=0}^n \binom{n}{k}$ combinatorially
63879
Prove that $\sum_{k=0}^r {m \choose k} {n \choose r-k} = {m+n \choose r}$
6366
Combinatorial proof of summation of $\sum\limits_{k = 0}^n {n \choose k}^2= {2n \choose n}$
123955
How to compute $\sum\limits_{k=0}^n (-1)^k{2n-k\choose k}$?
58264
How to derive the formula for the sum of the first $n$ perfect squares?
30518
Formula for $\sum_{k=1}^n \frac{1}{k(k+1)(k+2)}$?
101017
What is the sum of $\sum\limits_{i=1}^{n}ip^i$?
30472
Evaluate $\sum_{k=0}^{n} {n \choose k}{m \choose k}$ for a given $n$ and $m$.
87479
Closed form for $\sum_{k=0}^{n-p}\binom{n}{k}\binom{n}{p+k}$
68080
Evaluation of $\sum_{k=0}^n{n\choose k}^2u^k$
116722
Simplifying $\big(\sum_{i=0}^n\binom{k}{i}\binom{M-k}{n-i}\frac{k-i}{M-n}\big)/{\binom{M}{n}}$
54473
Value of $\sum 1/p^p$
127150
Finding general formula of $\sum_{i=0}^n i^2 \binom{n}{i}$
114173
Explanation of the formulas for sums $\sum nr^n$ and $\sum n^2 r^n$