Identity for a sum of binomial coefficients
14197
show that $\sum_{i=0}^l \dfrac{{l\choose i}}{{n\choose k + i}} = \dfrac{n+1}{(n-l+1) {n-l\choose k}}$
115686
A finite summation of double binomial coefficients
1139
Combinatorial proof of $\sum_{j=0}^{k} \binom{n}{j} = \sum_{j=0}^k \binom{n-1-j}{k-j}2^j$
58247
Prove $\sum_{k=0}^n \binom{n+k}{k}=\binom{2n+1}{n}$
7143
Identity for convolution of central binomial coefficients: $\sum\limits_{k=0}^n \binom{2k}{k}\binom{2(n-k)}{n-k}=2^{2n}$
83229
Nested summations and their relation to binomial coefficients
35342
Show that $ \sum_{n=2}^m \binom{n}{2} = \binom{m+1}{3}$
65983
Combinatorial proof of binomial coefficient summation identity
87505
binomial coefficient equal to sum
140140
An identity which applies to all of the natural numbers
146810
How to derive this binomial identity?
147910
Prove that $\sum_{n=0}^N\binom{2N-n}N2^n(n+1)=(1+2N)\binom{2N}N$
75910
Combinatorial Proof of Combinatorial Identity involving $(-1)^k \binom {n-1}{k}$
45862
Nested sum of binomial coefficient in closed form
116461
Prove the identity $\sum_{k=0}^{n}(-1)^{k}\binom{n}{k}=0$ using a combinatorial interpretation of the positive and negative terms
11335
Proving Binomial Identity without calculus
109576
Prove that $\binom{m+n}{m}=\sum\limits_{i=0}^m \binom{m}{i}\binom{n}{i}$