Prove $\sum_{n=0}^{N+1}P(n)(-1)^n\binom{N+1}{n}=0$ with degree at most $N$ of $P$
119999
A property of every real polynomial.
133181
Hint on how to prove the identity $\sum_{0 \leq k \leq n } \binom{k}{m} = \binom{n + 1}{m + 1}$
120074
Prove by Combinatorial Argument that $\binom{n}{k}= \frac{n}{k} \binom{n-1}{k-1}$
23557
Algebraic Proof that $\sum\limits_{i=0}^n \binom{n}{i}=2^n$
143337
How to prove that $\sum_{i=0}^n 2^i\binom{2n-i}{n} = 4^n$.
27922
prove that $\binom{n}{0}^2+\binom{n}{1}^2+\binom{n}{2}^2+\cdots+\binom{n}{n}^2=\binom{2n}{n}$
146762
Closed form for $\sum_{k=0}^{n} \binom{n}{k}\frac{(-1)^k}{(k+1)^2}$
5049
Proving $\sum_{k=0}^n(-1)^k\binom nk=0$
111505
Proof $\binom{p-1}{k}\equiv (-1)^k \mod{p}$
87479
Closed form for $\sum_{k=0}^{n-p}\binom{n}{k}\binom{n}{p+k}$
72026
Induction proof of $\sum_{k=1}^{n} \binom n k = 2^n -1 $
1158
How to prove this binomial identity $\sum_{r=0}^n {r {n \choose r}} = n2^{n-1}$?
9522
Proving $k \binom{n}{k} = n \binom{n-1}{k-1}$
59638
How to prove this result on binomial coefficients?
55266
Prove that $(n+1)^{n-1}<n^n$
19581
$\sum_{k=0}^n (-1)^k \binom{n}{k}^2$ and $\sum_{k=0}^n k \binom{n}{k}^2$
120976
Proving $\sum_{k=0}^{n}k{n\choose k}^2 = n{2n-1 \choose n-1} $