Proving a binomial series to be $2^n$
4991
Proving by induction that $ \sum_{k=0}^n{n \choose k} = 2^n$
1139
Combinatorial proof of $\sum_{j=0}^{k} \binom{n}{j} = \sum_{j=0}^k \binom{n-1-j}{k-j}2^j$
146533
Having problems proving $ \sum_{r=0}^{n}(r+1) \binom{n}{r} = (n+2)2^{n-1} $
146810
How to derive this binomial identity?
158774
Series of binomial coefficients: $\sum\limits_{n=k}^{\infty}{\binom nk}x^n=\frac{x^k}{(1-x)^{k+1}}$
64378
Proving a binomial sum identity $\sum _{k=0}^n \binom nk \frac{(-1)^k}{2k+1} = \frac{(2n)!!}{(2n+1)!!}$
92784
Intuitive (combinatorial) proof of $2^n=\sum_{k=0}^n {n\choose k}$
122005
Can $n(n+1)2^{n-2} = \sum_{i=1}^{n} i^2 \binom{n}{i}$ be derived from the binomial theorem?
111098
Prove $2^{2n} = \sum_{k=0}^{n}\binom{2n+1}{k}$
46840
How to prove that $\sum_{r=0}^n\binom{n}{r}2^r=3^n$
150355
Finding sum of binomial series
58247
Prove $\sum_{k=0}^n \binom{n+k}{k}=\binom{2n+1}{n}$
32791
Proving this binomial identity $\sum_{k=0}^n {n+k \choose k} \frac{1}{2^{k}}= 2^{n}$
151384
Summation of series involving binomial coefficients and polynomial of degree at most n-1
67844
Prove equation with binomial coefficient
13525
Prove: If $n=2^k-1$, then $\binom{n}{i}$ is odd for $0\leq i\leq n$
143927
Binomial coefficients that are powers of 2