Prove by induction that $\frac{n^3}{3}+\frac{2n}{3}$ is an integer.
106847
Proof that $n^3+2n$ is divisible by $3$
125618
Prove $2^{3^n}+1 $ is a multiple of $3^{n+1}$ by induction
106993
Use Complete Induction of set theory to prove $\frac{1}{\sqrt{1}} + \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{3}} + ... + \frac{1}{\sqrt{n}} > \sqrt{n}$.
68400
Proof that $\frac{(2n)!}{2^n}$ is integer
14064
Proof by induction that $\sum_{i=1}^n \frac{i}{(i+1)!}=1- \frac{1}{(n+1)!}$
128309
Use Mathematical Induction to prove that $\frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3} +...+\frac{1}{n(n+1)}=1-\frac{1}{n+1}$
42285
Prove by mathematical induction.
123195
Prove by induction that a^n+a^-n is an integer.
114212
How to use Mathematical Induction to prove $\frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3} + \cdots + \frac{1}{n(n + 1)} = \frac{n}{n + 1}$?
6488
Proof that $n^3 + 3n^2 + 2n$ is a multiple of $3$.
130093
Prove by Induction : $n < 2^n$
107824
Proof by induction that $a_0 = 1, a_1 = 1, a_n=2a_{n-1} + 3a_{n-2}$ satisfies $a_n = \frac12 (3^n) + \frac12 (-1)^n$
50599
Prove that $\frac{1}{1*3}+\frac{1}{3*5}+\frac{1}{5*7}+...+\frac{1}{(2n-1)(2n+1)}=\frac{n}{2n+1}$
4750
Show that for any positive integer n, $(3n)!/(3!)^n$ is an integer.
63652
Mathematical induction for inequalities: $\frac1{n+1} + \frac1{n+2} + \cdots +\frac1{3n+1} > 1$
6165
Proof by Induction $n^2+n$ is even
17714
Proof $\sum_{k=1}^n (-1)^{k+1} \binom{n}{k}\frac{1}{k} = H_n$ by induction