Proving that $4^n = { {{2n+1} \choose {0}} + {{2n+1} \choose {1}} + \;...\; + {{2n+1} \choose {n}}}$
55481
Prove the identity $\binom{2n+1}{0} + \binom{2n+1}{1} + \cdots + \binom{2n+1}{n} = 4^n$
70386
Proof by induction: $2^n > n^2$ for all integer $n$ greater than $4$
10629
How to prove $4(n!)>2^{n+2}$ for $ n\geq 4$ with induction
118372
Combination proof for $n(n+1)2^{n-2}=\sum_{k=1}^{n}k^2\binom{n}{k}$
66016
Prove $3^{2n+1} + 2^{n+2}$ is divisible by $7$ for all $n\ge0$
44161
Using induction to prove $\sum_{k=0}^{N-1} 2^k = 2^N-1$
58428
Proving $\sum_{k=0}^{n} {k \choose a} {n-k \choose b} = {n+1\choose a+b+1}$
71534
Combinatorial explanation for why $n^2 = {n \choose 2} + {n+1 \choose 2}$
2877
Show $\sum\limits_{n=0}^{\infty}{2n \choose n}x^n=(1-4x)^{-1/2}$
74730
Combinatorial Proof of ${{n}\choose{k}} {{k}\choose{j}} = {{n}\choose{j}} {{n-j}\choose{k-j}}$
24588
Proving the combinatorial identity ${n \choose k} = {n-2\choose k-2} + 2{n-2\choose k-1} + {n-2\choose k}$
89576
Proof of a binomial identity $\sum_{k=0}^n {n \choose k}^{\!2} = {2n \choose n}.$
6366
Combinatorial proof of summation of $\sum\limits_{k = 0}^n {n \choose k}^2= {2n \choose n}$
89175
Proof of $(a+b)^{n+1}$
130093
Prove by Induction : $n < 2^n$
157294
Prove that if $n>1$ is odd, then $1^n+2^n+3^n+\ldots+(n-1)^n$ is divisible by $n$
3043
Prove $n!>2^n$ for $n\geq4$ using induction.