The identity $a^n-b^n=(a-b) (\sum_{i=0}^{n-1}a^ib^{n-1-i})$
127293
Prove that $(a-b) \mid (a^n-b^n)$
58247
Prove $\sum_{k=0}^n \binom{n+k}{k}=\binom{2n+1}{n}$
39739
Fibonacci identity: $f_{n+1}f_{n-1} = f_n^2 + (-1)^n$
25648
Prove $(a_1+b_1)^{1/n}\cdots(a_n+b_n)^{1/n}\ge \left(a_1\cdots a_n\right)^{1/n}+\left(b_1\cdots b_n\right)^{1/n}$
89175
Proof of $(a+b)^{n+1}$
25826
Proof of a combinatorial identity: $\sum\limits_{i=0}^n {2i \choose i}{2(n-i)\choose n-i} = 4^n$
61483
Prove the following identity combinatorially
36388
How to derive this Combinatorial identity
75910
Combinatorial Proof of Combinatorial Identity involving $(-1)^k \binom {n-1}{k}$
44484
Combinatorial identity $i{n \choose i } =n {n-1 \choose i - 1}$
3798
Finding formula for sum $S_n = \sum_{i=1}^n i(i-1)$
10875
proof of binomial identity involving double sum
93085
How to prove the identity $\prod_{n=1}^{\infty} (1-q^{2n-1}) (1+q^{n}) =1 $ for $|q|<1$?
10777
Proof of the identity $2^n = \sum\limits_{k=0}^n 2^{-k} \binom{n+k}{k}$
142666
Algebric proof for the identity $n(n-1)2^{n-2}=\sum_{k=1}^n {k(k-1) {n \choose k}}$
65672
Proof of the summation $n!=\sum_{k=0}^n \binom{n}{k}(n-k+1)^n(-1)^k$?
52113
Proof by Induction $\sum_{i=0}^{k-1} 2^i = 2^k-1$