How to proof $\sum_{k=1}^n k {n \choose k }=n 2^{n-1}$
44111
Find the value of $\sum_{k=1}^{n}k\binom{n}{k}$?
114911
Evaluate $\sum_{k = 0}^{n} {n\choose k} k^m$
20317
Proving $\sum_{k=1}^{n}{(-1)^{k+1} {{n}\choose{k}}\frac{1}{k}=H_n}$
84010
Combinatorial proof that $\sum \limits_{k=0}^n \binom{2k}{k} \binom{2n-2k}{n-k} (-1)^k = 2^n \binom{n}{n/2}$ when $n$ is even
1125
Inductive proof that ${2n\choose n}=\sum{n\choose i}^2.$
92784
Intuitive (combinatorial) proof of $2^n=\sum_{k=0}^n {n\choose k}$
19571
Combinatorial proof for $\sum_{k = 0}^n \binom {r+k} k = \binom {r + n + 1} n$
63879
Prove that $\sum_{k=0}^r {m \choose k} {n \choose r-k} = {m+n \choose r}$
37650
Find $\sum_{m=0}^n\ (-1)^m m^n {n \choose m}$
24588
Proving the combinatorial identity ${n \choose k} = {n-2\choose k-2} + 2{n-2\choose k-1} + {n-2\choose k}$
133181
Hint on how to prove the identity $\sum_{0 \leq k \leq n } \binom{k}{m} = \binom{n + 1}{m + 1}$
75910
Combinatorial Proof of Combinatorial Identity involving $(-1)^k \binom {n-1}{k}$
147910
Prove that $\sum_{n=0}^N\binom{2N-n}N2^n(n+1)=(1+2N)\binom{2N}N$
139842
Seeking a combinatorial proof $\sum\limits _{k=0}^n (n-2k)^2\binom{n}{k}=n\times 2^n$
30338
How to prove that $\sum_{k=0}^n \binom nk k^2=2^{n-2}(n^2+n)$
44328
Prove that $\sum_{k=1} ^ n k^{-1} = \ln(n) + O(1)$
123955
How to compute $\sum\limits_{k=0}^n (-1)^k{2n-k\choose k}$?