Induction based on combinations and binomial theorem: ${}^nC_0+{}^{n+1}C_1+{}^{n+2}C_2+\dots+{}^{n+p}C_p={}^{n+p+1}C_p$
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Proof of the Hockey-Stick Identity: $\sum\limits_{t=0}^n \binom tk = \binom{n+1}{k+1}$
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Proof by Induction: $\sum_0^nx^i=(1-x^{n+1})/(1-x)$
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Proof $\sum_{k=1}^n (-1)^{k+1} \binom{n}{k}\frac{1}{k} = H_n$ by induction
71918
Mathematical Induction
33082
Proving $\sum_{i=0}^n 2^i=2^{n+1}-1$ by induction.
42105
Fibonacci proof by induction
127205
Explain proof of irreducibility of $x^{p-1} + 2x^{p-2}+ \dots +(p-1)x + p$
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Proving by induction that $ \sum_{k=0}^n{n \choose k} = 2^n$
108274
Sum of the first $n$ triangular numbers - induction
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Prove by Mathematical Induction: $1(1!) + 2(2!) + \cdot \cdot \cdot +n(n!) = (n+1)!-1$
92704
Prove that $\sum_{k=1}^{n}k\binom{n}{k}=n\cdot2^{n-1}$
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Use Mathematical Induction to prove that $\frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3} +...+\frac{1}{n(n+1)}=1-\frac{1}{n+1}$
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proof by induction: sum of binomial coefficients $\sum_{k=0}^n (^n_k) = 2^n$
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Fibonacci numbers and proof by induction
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Revisited: Binomial Theorem: An Inductive Proof
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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
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Proving $\frac{1}{n+1} + \frac{1}{n+2}+\cdots+\frac{1}{2n} > \frac{13}{24}$ for $n>1,n\in\Bbb N$ by Induction