Prove by induction that $\sum_{i=1}^{n} 2i=(n+1)n$, for every positive integer n.
2675
Proof $1+2+3+4+\cdots+n = \frac{n\times(n+1)}2$
141446
Proving by induction that $\sum\limits_{k=2}^n \frac1{k^2}\le 1$
88055
Use induction to prove the following: $1! + 2! + .... + n! \le (n + 1)!$
121544
Proof by Induction: $2(\sqrt{n+1} - \sqrt{n}) < \frac{1}{\sqrt{n}} < 2(\sqrt{n}-\sqrt{n-1})$
62556
Prove $3|n(n+1)(n+2)$ by induction
142992
Prove that for every positive integer $n$, $1/1^2+1/2^2+1/3^2+\cdots+1/n^2\le2-1/n$
88292
Prove by induction that $\sum\limits_{i=1}^n \frac{1}{n+i} \leq \frac{3}{4}$
11642
Proving by induction that $2^n \le 2^{n+1}-2^{n-1} - 1$ . Does my proof make sense?
62177
Prove that: $2^n < n!$ Using Induction
25826
Proof of a combinatorial identity: $\sum\limits_{i=0}^n {2i \choose i}{2(n-i)\choose n-i} = 4^n$
121107
Proof by induction: $n^{n+1} > (n + 1)^n$, $(1 + x)^n \ge 1 + nx$, other inequalities
17714
Proof $\sum_{k=1}^n (-1)^{k+1} \binom{n}{k}\frac{1}{k} = H_n$ by induction
2885
Prove that $\sum\limits_{i=1}^n 2i\binom{2n}{n-i}= n\binom{2n}{n}$
73938
Prove that $\sum_{r=1}^nr(r+1)=\frac{n(n+1)(n+2)}{3}$ using induction
66578
Prove by induction that $2^{2n} – 1$ is divisible by $3$ whenever n is a positive integer.
90789
Use induction to prove that that $8^{n} | (4n)!$ for all positive integers $n$
70625
Prove By Induction $1 + 1/2 + 1/3 + ... + 1/(2^n) ≥ 1 + n/2$