Evaluate $\sum_{i=0}^{100}\binom{k}{i}\binom{M-k}{100-i}\frac{k-i}{M-100}.$
116722
Simplifying $\big(\sum_{i=0}^n\binom{k}{i}\binom{M-k}{n-i}\frac{k-i}{M-n}\big)/{\binom{M}{n}}$
127150
Finding general formula of $\sum_{i=0}^n i^2 \binom{n}{i}$
117200
Evaluation of $ \sum_{k=0}^n \cos k\theta $
74294
How to simplify $\sum_{i=1}^{k}\binom{n + i - 1}{i}$?
109640
How do i find $(1+i)^{100}?$
98082
Another combinatorics problem: $\sum\limits_{k = 0}^n (-1)^k \binom{2n-k}k2^{2n-2k}=2n+1$
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} $
72639
Show that $\sum_{k=0}^n\binom{3n}{3k}=\frac{8^n+2(-1)^n}{3}$
94060
Sum of square binomial coefficients
79814
Calculate sums of inverses of binomial coefficients
9046
Prove that $\sum_{k=0}^{m}\frac{\binom{m}{k}}{\binom{n}{k}}=\frac{n+1}{n+1-m}$
48200
Simplify $\sum_{i=0}^n (i+1)\binom ni$
99249
Sum of product of binomial coefficients: $\sum_{k=0}^{n}(-1)^k\binom{n}{k}\binom{n + k}{k} = (-1)^n$
8806
Summation of binomial coefficients
116461
Prove the identity $\sum_{k=0}^{n}(-1)^{k}\binom{n}{k}=0$ using a combinatorial interpretation of the positive and negative terms
17638
Sum with binomial coefficients: $\sum_{k=0}^{n}{2n\choose 2k}$
37650
Find $\sum_{m=0}^n\ (-1)^m m^n {n \choose m}$