Proving $\sum_{k=1}^n\binom{n}kk=n\,2^{n-1}$
54442
Sum of $k {n \choose k}$ is $n2^{n-1}$
1258
Prove $3^n = \sum_{k=0}^n \binom {n} {k} 2^k$
92704
Prove that $\sum_{k=1}^{n}k\binom{n}{k}=n\cdot2^{n-1}$
9522
Proving $k \binom{n}{k} = n \binom{n-1}{k-1}$
13236
Proving equality - a sum including binomial coefficient $\sum_{k=1}^{n}k{n \choose k}2^{n-k}=n3^{n-1}$
345
Proving $ \sum _{k=0} ^m \binom nk \binom{n-k}{m-k} = 2^m \binom {n}{m}$.
145524
Proving this identity $\sum_k\frac{1}{k}\binom{2k-2}{k-1}\binom{2n-2k+1}{n-k}=\binom{2n}{n-1}$ using lattice paths
121279
Proving an Combination formula $ \binom{n}{k} = \binom{n-1}{k}+\binom{n-1}{k-1}$
30338
How to prove that $\sum_{k=0}^n \binom nk k^2=2^{n-2}(n^2+n)$
2885
Prove that $\sum\limits_{i=1}^n 2i\binom{2n}{n-i}= n\binom{2n}{n}$
1158
How to prove this binomial identity $\sum_{r=0}^n {r {n \choose r}} = n2^{n-1}$?
111098
Prove $2^{2n} = \sum_{k=0}^{n}\binom{2n+1}{k}$
46840
How to prove that $\sum_{r=0}^n\binom{n}{r}2^r=3^n$
143337
How to prove that $\sum_{i=0}^n 2^i\binom{2n-i}{n} = 4^n$.
11612
How to show that $\sum_{k=1}^n k(n+1-k)=\binom{n+2}3$?
133181
Hint on how to prove the identity $\sum_{0 \leq k \leq n } \binom{k}{m} = \binom{n + 1}{m + 1}$
113321
Hint proving this $\sum_{k=0}^{n}\binom{2n}{k}k=n2^{2n-1}$