Prove the identity $\sum_{k=0}^n \binom{n}{k}=2^n.$ using combinatorial proof
104704
Evaluate $\sum\limits_{k=0}^n \binom{n}{k}$ combinatorially
129304
Alternative combinatorial proof for $\sum\limits_{r=0}^n\binom{n}{r}\binom{m+r}{n}=\sum\limits_{r=0}^n\binom{n}{r}\binom{m}{r}2^r$
67927
Combinatorial argument for the identity $k\binom{n}{k} = n\binom{n-1}{k-1}$
65983
Combinatorial proof of binomial coefficient summation identity
60860
Combinatorial proof of $\sum_{i = 0}^{n} \binom{i}{r - 1} = \binom{n + 1}{r}$ and then use result to find a formula for $1^2 + 2^2 + \ldots + n^2$
89552
proving combinatorics identity - $\sum_{k=0}^m{n-k \choose m-k}={n+1 \choose m}$
108401
Sum of binomial coefficients $\sum_{k=0}^{n}(-1)^k\binom{n}{k}\binom{2n - 2k}{n - 1} = 0$
111098
Prove $2^{2n} = \sum_{k=0}^{n}\binom{2n+1}{k}$
71564
Combinatorial proof of identity involving central binomial coefficients
30414
Prove using combinatorics $\sum\limits_{k=0}^n 2^k \binom{n}{k} \binom{n-k}{\lfloor{\frac{n-k}{2}}\rfloor}=\binom{2n+1}{n}$
136580
Proving $\sum_{k=0}^n\binom{2n}{2k} = 2^{2n-1}$
118372
Combination proof for $n(n+1)2^{n-2}=\sum_{k=1}^{n}k^2\binom{n}{k}$
4201
Prove $\sum\binom{n}{k}2^k = 3^n$ using the binomial theorem
133181
Hint on how to prove the identity $\sum_{0 \leq k \leq n } \binom{k}{m} = \binom{n + 1}{m + 1}$
1258
Prove $3^n = \sum_{k=0}^n \binom {n} {k} 2^k$
130223
Proving a special case of the binomial theorem: $\sum^{k}_{m=0}\binom{k}{m} = 2^k$
70128
Prove that $(fg)^{(n)} = \sum_{k=0}^n \binom{n}{k}f^{(k)}(x)g^{(n-k)}(x)$