Using induction to verify the formula for a summation $\sum_{k=1}^n k^2 = \frac{n(n+1)(2n+1)}6$
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induction proof: $\sum_{k=1}^nk^2 = \frac{n(n+1)(2n+1)}{6}$
79652
Proof by induction that $2 + 4 + 6 + \cdots + 2n = n(n+1)$
9435
Prove that $1^2+2^2+\cdots+n^2=\frac{n(n+1)(2n+1)}{6}$ for $n \in \mathbb{N}$.
136737
Proof by Induction for inequality, $\sum_{k=1}^nk^{-2}\lt2-(1/n)$
16776
How to prove $\sum_{m=1}^\infty \sum_{n=1}^\infty \frac{1}{m^2+n^2}=+\infty$
146200
proof by induction: sum of binomial coefficients $\sum_{k=0}^n (^n_k) = 2^n$
139074
Question about $a_n=\sum_{k=1}^n \frac{n}{n^2+k}\ $for $ n \in\mathbb{N}$
5272
Proving that $\sum_{k=0}^{n}\frac{(-1)^k}{{n\choose k}}=[1+(-1)^n] \frac{n+1}{n+2}.$
52113
Proof by Induction $\sum_{i=0}^{k-1} 2^i = 2^k-1$
148330
Induction Proof for $F_{2n} = F^2_{n+1} - F^2_{n-1}$
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Help with proof using induction: $1 + \frac{1}{4} + \frac{1}{9}+\cdots+\frac{1}{n^2}\leq 2-\frac{1}{n}$
16812
Proving $1^3+ 2^3 + \cdots + n^3 = \left(\frac{n(n+1)}{2}\right)^2$ using induction
10976
Using induction to prove that $\sum_{r=1}^n r\cdot r! =(n+1)! -1$
138542
Evaluating sums question $\sum_{k=2}^n \frac{1}{k^2-1}$
131565
Proof by induction of summation inequality: $1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\dots+\frac1{2^n}\ge 1+\frac{n}2$
89367
Calculate $ S =\sum_{k=1}^n\frac {1}{k(k+1)(k+2)}. $
92440
Let $n \in \mathbb{Z}^+$, prove the identity $ \sum_{k=1}^{n-1} \binom {n} {k} \frac{kn^{n-k}}{k+1}=\frac{n(n^{n}-1)}{n+1}$