Prove for all whole numbers n, $(n+1)(n+2)...(2n-1)(2n)=2^n(1)(3)(5)...(2n-1)$
94389
Proving formula for product of first n odd numbers
62177
Prove that: $2^n < n!$ Using Induction
55428
Inductive proof of $a_n = 3*2^{n-1} + 2(-1)^n$ if $a_n = a_{n-1} + 2*a_{n-2}, a_1 = 1, a_2 = 8$
50599
Prove that $\frac{1}{1*3}+\frac{1}{3*5}+\frac{1}{5*7}+...+\frac{1}{(2n-1)(2n+1)}=\frac{n}{2n+1}$
111298
Direct Proof that $1 + 3 + 5 + \cdots+ (2n - 1) = n\cdot n$
17491
Proof by Induction: Solving $1+3+5+\cdots+(2n-1)$
100305
Prove $2^n-1$ is divisible by $(2^m-1)^2$ iff...
27580
Use mathematical induction to prove $ (2n)!\geq 2^n(n!)^2$ for $n \in \mathbb{N}$
114867
Prove $\forall n\geq 2,n\in\mathbb{Z}$, $(n+1)\mid(n^3+1)$
122019
Prove by mathematical induction that $2^{3^n}+1$ is divisible by $3^{n+1}$
48081
Prove that for all $n \in \mathbb{N}$: $2^{n-1}(a^n + b^n) \ge (a + b)^n$
31344
Proving $2^{2^n}+3^{2^n}+5^{2^n}$ is divisible by $19$ for all $n\geq 1$ by induction
50894
Prove that $6$ divides $n(n + 1)(n + 2)$
26514
Prove that if $n$ is a composite, then $2^n-1$ is composite.
34059
$(a^{2^n}+1,a^{2^m}+1)=1 or 2$
55266
Prove that $(n+1)^{n-1}<n^n$
130093
Prove by Induction : $n < 2^n$