How to prove $\sum_{k=1}^n(2k)^2 = \frac{2n(n+1)(2n+1)}{3}$ using mathematical induction?
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induction proof: $\sum_{k=1}^nk^2 = \frac{n(n+1)(2n+1)}{6}$
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Proving by induction that $\sum\limits_{k=2}^n \frac1{k^2}\le 1$
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Proof by Induction $\sum_{i=0}^{k-1} 2^i = 2^k-1$
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Double induction example: $ 1 + q + q^2 + q^3 + \cdots + q^{n-1} + q^n = \frac {q^{n+1}-1}{q-1} $
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Proof by Induction: Solving $1+3+5+\cdots+(2n-1)$
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Summation inductional proof: $\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+\ldots+\frac{1}{n^2}<2$
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Proving the sum of the first $n$ natural numbers by induction
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How to prove $\sum_{k=1}^{n}F_k = F_{n+2}-1$ by induction when $F_n$ is the Fibonacci sequence
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Combination proof for $n(n+1)2^{n-2}=\sum_{k=1}^{n}k^2\binom{n}{k}$
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Proving a binomial sum identity $\sum _{k=0}^n \binom nk \frac{(-1)^k}{2k+1} = \frac{(2n)!!}{(2n+1)!!}$
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Show by induction: $(1+\frac{1}{n})^{n}<n$
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Proof by induction: $\sum\limits_{i=1}^{n} \frac{1}{n+i} = \sum\limits_{i=1}^{n} \left(\frac{1}{2i-1} - \frac{1}{2i}\right)$
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Proof by Induction: $2(\sqrt{n+1} - \sqrt{n}) < \frac{1}{\sqrt{n}} < 2(\sqrt{n}-\sqrt{n-1})$
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proof by induction: sum of binomial coefficients $\sum_{k=0}^n (^n_k) = 2^n$
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Formula for $\sum_{k=1}^n \frac{1}{k(k+1)(k+2)}$?
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Proving $\sum\limits_{i=0}^n  i 2^{i-1} = (n+1) 2^n - 1$ by induction
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How to proof that $\forall n \ge 1: \sum_{i=1}^n (i(i+1))^{-1} = n(n+1)^{-1}$ using mathematical induction