Proof by induction for $\left(1−\frac14\right)\cdot\left(1−\frac19\right)\cdots\left(1−\frac1{n^2}\right)$ for all natural numbers $n$ with $n \ge 2$
138683
Proving $\prod_{i=2}^{i=n} \left(1-\frac{1}{i^2}\right) = \frac{n+1}{2n}$ by induction
73892
Prove $Σ_{cyc}\frac{1}{\left(a+1\right)^2}+\frac{1}{a+b+c+1}\ge 1$
73002
For $n \geq 2$, prove that $(1- \frac{1}{4})(1- \frac{1}{9})(1- \frac{1}{16})...(1- \frac{1}{n^2}) = \frac{n+1}{2n}$
142992
Prove that for every positive integer $n$, $1/1^2+1/2^2+1/3^2+\cdots+1/n^2\le2-1/n$
115912
Summation inductional proof: $\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+\ldots+\frac{1}{n^2}<2$
62556
Prove $3|n(n+1)(n+2)$ by induction
48333
Prove by induction that $(x+1)^n - nx - 1$ is divisible by $x^2$
79657
Prove by induction $\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}{4}$ for $n\ge1$
96366
show that for any n $\in$ $\Bbb N$ , if n $\ge$ 2, then $\prod_\limits{i=2}^n $ $\left( 1-\frac{1}{i^2}\right)$ = $\frac{n+1}{2n}$
72026
Induction proof of $\sum_{k=1}^{n} \binom n k = 2^n -1 $
14064
Proof by induction that $\sum_{i=1}^n \frac{i}{(i+1)!}=1- \frac{1}{(n+1)!}$
101899
Proof By Induction of a Sum
155562
Proving $\sum_{k=1}^nk^3 = \left(\sum_{k=1}^n k\right)^2$ using complete induction
54595
Prove $\sum\limits_{i=2}^{n}\frac{1}{(i-1)i}$ = $\frac{(n-1)}{n}$ using induction.
124584
How to proof that $\forall n \ge 1: \sum_{i=1}^n (i(i+1))^{-1} = n(n+1)^{-1}$ using mathematical induction
66996
Proof by induction of Bernoulli's inequality $ (1+x)^n \ge 1+nx$
14435
Show by induction: $(1+\frac{1}{n})^{n}<n$