Binomial coefficients with sums
72639
Show that $\sum_{k=0}^n\binom{3n}{3k}=\frac{8^n+2(-1)^n}{3}$
64803
Counting two ways, $\sum \binom{n}{k} \binom{m}{n-k} = \binom{n+m}{n}$
7083
Alternating sum of binomial coefficients: given $n \in \mathbb N$, prove $\sum^n_{k=0}(-1)^k {n \choose k} = 0$
44111
Find the value of $\sum_{k=1}^{n}k\binom{n}{k}$?
1139
Combinatorial proof of $\sum_{j=0}^{k} \binom{n}{j} = \sum_{j=0}^k \binom{n-1-j}{k-j}2^j$
151384
Summation of series involving binomial coefficients and polynomial of degree at most n-1
19571
Combinatorial proof for $\sum_{k = 0}^n \binom {r+k} k = \binom {r + n + 1} n$
17638
Sum with binomial coefficients: $\sum_{k=0}^{n}{2n\choose 2k}$
146762
Closed form for $\sum_{k=0}^{n} \binom{n}{k}\frac{(-1)^k}{(k+1)^2}$
144571
A conjecture including binomial coefficients
126587
Divisiblity of binomial coefficients
150355
Finding sum of binomial series
125712
Working with binomial coefficient $\sum_{k=0}^n (-1)^k \binom nk=0$
152845
Every integer is the unique sum of a "decreasing" sequence of binomial coefficients
42606
Orthogonality for Binomial Coefficients
109576
Prove that $\binom{m+n}{m}=\sum\limits_{i=0}^m \binom{m}{i}\binom{n}{i}$
130223
Proving a special case of the binomial theorem: $\sum^{k}_{m=0}\binom{k}{m} = 2^k$