Alternating sum of binomial coefficients is equal to zero
7083
Alternating sum of binomial coefficients: given $n \in \mathbb N$, prove $\sum^n_{k=0}(-1)^k {n \choose k} = 0$
83229
Nested summations and their relation to binomial coefficients
5332
Find the value of $\sum_0^n \binom{n}{k} (-1)^k \frac{1}{k+1}$
91239
Sum of binomial coefficients involving $n,p,q,r$
14399
Calculate $\sum_{k=1}^n (-1)^{k+1} \binom{n}{k}\frac{1}{k}$
63510
Prove: $\binom{n}{k}^{-1}=(n+1)\int_{0}^{1}x^{k}(1-x)^{n-k}dx$ for $0 \leq k \leq n$
89279
If $\sum a_n/k^n = 0$ for all $k$, then $a_n = 0$ for all $n$
118571
Why is $\sum\limits_{k=0}^{n}(-1)^k\binom{n}{k}^2=(-1)^{n/2}\binom{n}{n/2}$ if $n$ is even?
79124
Proving $\binom {n-1}{r-1}=\sum_{k=0}^r(-1)^k\binom r k \binom{n+r-k-1}{r-k-1}$
125220
Solving binomial theorem via induction
142303
Alternating sum of binomial coefficients multiplied by (1/k+1)
122024
Asymptotic of a sum involving binomial coefficients
98082
Another combinatorics problem: $\sum\limits_{k = 0}^n (-1)^k \binom{2n-k}k2^{2n-2k}=2n+1$
87505
binomial coefficient equal to sum
49234
Sum of binomial coefficients with index divisible by 4
145582
$\sum (-1)^n/n$ fails the p-series test, but passes the alternating series test?
130223
Proving a special case of the binomial theorem: $\sum^{k}_{m=0}\binom{k}{m} = 2^k$