Proving an Identity involving $4^N$
7143
Identity for convolution of central binomial coefficients: $\sum\limits_{k=0}^n \binom{2k}{k}\binom{2(n-k)}{n-k}=2^{2n}$
62177
Prove that: $2^n < n!$ Using Induction
106888
Factorial identity $n!=1+(1-1/1!)n+(1-1/1!+1/2!)n(n-1)+\cdots$
71014
Prove that 2(nC0+nC2...nC$\frac{(N-1)}{2}$=$2^n$
146053
Proving identities (mod $pq$) using Fermat's little theorem?
11867
Prove by induction that $n < 2^n$ for all $n \ge 1$
122006
Proving combinatorial identity $\sum_{k=0}^{n}(-1)^k \binom{2n-k}k 2^{2n-2k} = 2n+1$ "directly"
89175
Proof of $(a+b)^{n+1}$
100788
Proving Newton's identities
44161
Using induction to prove $\sum_{k=0}^{N-1} 2^k = 2^N-1$
124240
Inductive proof of $\,9 \mathrel| 4^n+6n-1\,$ for all $\,n\in\Bbb N$
109648
Proving an identity for Bernoulli polynomials
92440
Let $n \in \mathbb{Z}^+$, prove the identity $ \sum_{k=1}^{n-1} \binom {n} {k} \frac{kn^{n-k}}{k+1}=\frac{n(n^{n}-1)}{n+1}$
153295
Algebraic Identity $a^{n}-b^{n} = (a-b) \sum\limits_{k=0}^{n-1} a^{k}b^{n-1-k}$
1158
How to prove this binomial identity $\sum_{r=0}^n {r {n \choose r}} = n2^{n-1}$?
111267
Prove that: $2^a+3^b<3a+4b$
147910
Prove that $\sum_{n=0}^N\binom{2N-n}N2^n(n+1)=(1+2N)\binom{2N}N$