Prove by induction that $1+3+3^2+3^3+...+3^n=\frac{1}{2}(3^{n+1}-1)$
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Simplifying a geometric sum
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Use induction to prove the following: $1! + 2! + .... + n! \le (n + 1)!$
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Proof by induction: $n^{n+1} > (n + 1)^n$, $(1 + x)^n \ge 1 + nx$, other inequalities
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Prove that $\frac{1}{n}+\frac{1}{n+1}+\frac{1}{n+2}+....+\frac{1}{2n}\geq \frac{2}{3}$
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Prove by induction that $\sqrt[n+1]{n+1}<\sqrt[n]{n}$ for $n\ge 3$
156356
Proof that $x^n+\frac{1}{x^n}\in \mathbb Z$ by complete induction
48333
Prove by induction that $(x+1)^n - nx - 1$ is divisible by $x^2$
38995
Induction proof that $\sum_{j=n}^{2n-1} (2j + 1) = 3n^2$ - what happened?
11407
Proving the summation formula using induction: $\sum_{k=1}^n \frac{1}{k(k+1)} = 1-\frac{1}{n+1}$
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Proof by induction that $\sum_{i=1}^n \frac{i}{(i+1)!}=1- \frac{1}{(n+1)!}$
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Proof by induction that $2 + 4 + 6 + \cdots + 2n = n(n+1)$
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How to Prove with Mathematical Induction $3^n > n^2$
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Prove by induction $\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}{4}$ for $n\ge1$
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Prove by induction $\sum \frac {1}{2^n} < 1$
33082
Proving $\sum_{i=0}^n 2^i=2^{n+1}-1$ by induction.
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Prove $3|n(n+1)(n+2)$ by induction
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Proof of the formula $1+x+x^2+x^3+ \cdots +x^n =\frac{x^{n+1}-1}{x-1}$