How to solve $\binom{n+m}{k} = \sum_{i=0}^{k} \binom{m}{i} \binom{n}{k-i} $
42763
How to prove Vandermonde's Identity: $\sum_{k=0}^{n}\binom{R}{k}\binom{M}{n-k}=\binom{R+M}{n}$?
158508
Combinatorial Proof for Binomial Identity: $\sum_{k = 0}^n \binom{k}{p} = \binom{n+1}{p+1}$
58247
Prove $\sum_{k=0}^n \binom{n+k}{k}=\binom{2n+1}{n}$
17638
Sum with binomial coefficients: $\sum_{k=0}^{n}{2n\choose 2k}$
32791
Proving this binomial identity $\sum_{k=0}^n {n+k \choose k} \frac{1}{2^{k}}= 2^{n}$
143047
find $\sum_{k=0}^{t}(-1)^k\binom{t}{k}^2$ for odd t then for even t
44111
Find the value of $\sum_{k=1}^{n}k\binom{n}{k}$?
126001
Prove by Double Counting Method $\sum\limits_{k = 0}^m \binom{m}{k}\binom{n}{r + k} = \binom{m + n}{m + r}$
112374
Evaluate $ \binom{n}{0}+\binom{n}{2}+\binom{n}{4}+\cdots+\binom{n}{2k}+\cdots$
145048
Prove $\sum_{k = 0}^{n}(-1)^{n - k} \binom{n}{k} \cdot k^n = n!$ and $\sum_{k = 0}^{n}(-1)^{n - k} \binom{n}{k} \cdot k^m = 0$
131326
How to find $\sum_{r\ge 0} \binom{n}{r}\binom{n-r}{r} 2^{n-2r}$?
8806
Summation of binomial coefficients
104704
Evaluate $\sum\limits_{k=0}^n \binom{n}{k}$ combinatorially
35342
Show that $ \sum_{n=2}^m \binom{n}{2} = \binom{m+1}{3}$
39199
closed form for $\binom{n}{0}+\binom{n}{3}+\binom{n}{6}+...+\binom{n}{n}$
110441
Closed form for a formula with a summation over $i\binom{n-i}{k-1}$, and combinatorial proof?
74294
How to simplify $\sum_{i=1}^{k}\binom{n + i - 1}{i}$?