Alternating sum of binomial coefficients equal to $1$
5049
Proving $\sum_{k=0}^n(-1)^k\binom nk=0$
17638
Sum with binomial coefficients: $\sum_{k=0}^{n}{2n\choose 2k}$
148949
Find the value of $\sum_{k=1}^{n} k \binom {n} {k}$
12812
Sum of the alternating harmonic series $\sum_{k=1}^{\infty}\frac{(-1)^{k+1}}{k} = \frac{1}{1} - \frac{1}{2} + \cdots $
15666
explanation for a combinatorial identity involving the binomial coefficient
112827
Find the sum of the binomial coefficients
132249
Sum of every $k$th binomial coefficient.
31970
Alternating sum of squares of binomial coefficients
133905
Intuitive proof of $\sum_{k=1}^{n} \binom{n}{k} k^{k-1} (n-k)^{n-k} = n^n$
151384
Summation of series involving binomial coefficients and polynomial of degree at most n-1
96945
General formula of $\sum_{n\ge1}{\binom{2n}{n}^{-k}}$.
107810
Induction with Binomial Coefficients
75910
Combinatorial Proof of Combinatorial Identity involving $(-1)^k \binom {n-1}{k}$
99249
Sum of product of binomial coefficients: $\sum_{k=0}^{n}(-1)^k\binom{n}{k}\binom{n + k}{k} = (-1)^n$
56828
A combinatorial proof that the alternating sum of binomial coefficients is zero
154280
Show this equality (The factorial as an alternate sum with binomial coefficients).
143047
find $\sum_{k=0}^{t}(-1)^k\binom{t}{k}^2$ for odd t then for even t