Show, with induction that $1^2 + 2^2 + .... + n^2 = \frac{n(n+1)(2n+1)}{6}$
26901
induction proof: $\sum_{k=1}^nk^2 = \frac{n(n+1)(2n+1)}{6}$
96894
Prove $f_{n+1}^2+f_n^2=f_{2n+1}$
14064
Proof by induction that $\sum_{i=1}^n \frac{i}{(i+1)!}=1- \frac{1}{(n+1)!}$
44928
Show $\sum_n \frac{z^{2^n}}{1-z^{2^{n+1}}} = \frac{z}{1-z}$
142132
How do you prove $\sum \frac {n}{2^n} = 2$?
150462
Prove by induction that for every $n \ge 0$ the term $2^{2n+1} - 9n^2 + 3n -2$ is divisible by $54$
145274
Prove by induction $\sum \frac {1}{2^n} < 1$
71014
Prove that 2(nC0+nC2...nC$\frac{(N-1)}{2}$=$2^n$
78583
Help with proof using induction: $1 + \frac{1}{4} + \frac{1}{9}+\cdots+\frac{1}{n^2}\leq 2-\frac{1}{n}$
81842
How to prove by induction that $\frac{a^n+b^n}{2}\geq\left(\frac{a+b}{2}\right)^n$?
124584
How to proof that $\forall n \ge 1: \sum_{i=1}^n (i(i+1))^{-1} = n(n+1)^{-1}$ using mathematical induction
27304
Proving $ 1+\frac{1}{4}+\frac{1}{9}+\cdots+\frac{1}{n^2}\leq 2-\frac{1}{n}$ for all $n\geq 2$ by induction
121544
Proof by Induction: $2(\sqrt{n+1} - \sqrt{n}) < \frac{1}{\sqrt{n}} < 2(\sqrt{n}-\sqrt{n-1})$
65315
Showing $1+2+\cdots+n=\frac{n(n+1)}{2}$ by induction (stuck on inductive step)
73938
Prove that $\sum_{r=1}^nr(r+1)=\frac{n(n+1)(n+2)}{3}$ using induction
54595
Prove $\sum\limits_{i=2}^{n}\frac{1}{(i-1)i}$ = $\frac{(n-1)}{n}$ using induction.
112907
Math Induction Proof: $(1+\frac1n)^n < n$