Alternating sum of binomial coefficients $1 - \binom{n}{2} + \binom{n}{4} - \binom{n}{6} + ...$
439
Alternating binomial sum with intervals of two
44111
Find the value of $\sum_{k=1}^{n}k\binom{n}{k}$?
44621
Simple binomial theorem proof: $\sum_{j=0}^{k} \binom{a+j}j = \binom{a+k+1}k$
158508
Combinatorial Proof for Binomial Identity: $\sum_{k = 0}^n \binom{k}{p} = \binom{n+1}{p+1}$
116491
Closed form for $\sum_{k=0}^{m} {\binom {m}{k}} a^{k} (b+ck)^N$
94060
Sum of square binomial coefficients
14399
Calculate $\sum_{k=1}^n (-1)^{k+1} \binom{n}{k}\frac{1}{k}$
84010
Combinatorial proof that $\sum \limits_{k=0}^n \binom{2k}{k} \binom{2n-2k}{n-k} (-1)^k = 2^n \binom{n}{n/2}$ when $n$ is even
92704
Prove that $\sum_{k=1}^{n}k\binom{n}{k}=n\cdot2^{n-1}$
65983
Combinatorial proof of binomial coefficient summation identity
39199
closed form for $\binom{n}{0}+\binom{n}{3}+\binom{n}{6}+...+\binom{n}{n}$
116461
Prove the identity $\sum_{k=0}^{n}(-1)^{k}\binom{n}{k}=0$ using a combinatorial interpretation of the positive and negative terms
99249
Sum of product of binomial coefficients: $\sum_{k=0}^{n}(-1)^k\binom{n}{k}\binom{n + k}{k} = (-1)^n$
128913
A proof of $\sum_{i=1}^{n}(-1)^{i-1}\binom{n}{i}\frac{1}{i}=\frac{1}{1}+\frac{1}{2}+....+\frac{1}{n}$
32260
Alternating Sum of Cubes
34803
Evaluating even binomial coefficients
11612
How to show that $\sum_{k=1}^n k(n+1-k)=\binom{n+2}3$?