Summation of binomial coefficients
626
Sum of combinations with varying $n$
83400
Sum of products of binomial coefficients: $ \sum_{l=0}^{n-j} \binom{M-1+l}{l} \binom{n-M-l}{n-j-l} = \binom{n}{j} $
125148
Summation of series $\sum_{k=0}^\infty 2^k/\binom{2k+1}{k}$
87589
Evaluate $\binom{n}{0}+\binom{n}{2}+\binom{n}{4}+...+\binom{n}{2k}$
35342
Show that $ \sum_{n=2}^m \binom{n}{2} = \binom{m+1}{3}$
35381
Sum with binomial coefficients: $\sum_{k=1}^m  \frac{1}{k}{m \choose k} $
14239
How to show $\sum_{k=0}^{n}\binom{n+k}{k}\frac{1}{2^k}=2^{n}$
45862
Nested sum of binomial coefficient in closed form
86194
Infinite series with the binomial coefficient
150355
Finding sum of binomial series
57549
Finding the sum $\sum_{k=1}^rk^2\binom {n-k}{r-k}$
99249
Sum of product of binomial coefficients: $\sum_{k=0}^{n}(-1)^k\binom{n}{k}\binom{n + k}{k} = (-1)^n$
42606
Orthogonality for Binomial Coefficients
155479
Summation of inner products
74294
How to simplify $\sum_{i=1}^{k}\binom{n + i - 1}{i}$?
122024
Asymptotic of a sum involving binomial coefficients
112374
Evaluate $ \binom{n}{0}+\binom{n}{2}+\binom{n}{4}+\cdots+\binom{n}{2k}+\cdots$