Prove by induction that the $n$th iterate of $\frac{x}{\sqrt{1+x^2}}$ is $\frac{x}{\sqrt{1+nx^2}}$
134181
What is the $n$ times iterate of $f(x)=\frac{x}{\sqrt{1+x^2}}$?
22073
Prove by induction that $n^2<n!$
155897
Proof by induction - is this correct?
14064
Proof by induction that $\sum_{i=1}^n \frac{i}{(i+1)!}=1- \frac{1}{(n+1)!}$
143236
$ S_{n}=\frac{x}{x+1}+\frac{x^2}{(x+1)(x^2+1)}+...........+\frac{x^{2^{n}}}{(x+1)(x^2+1)...(x^{2^{n}}+1)}$
95000
Using induction to prove that $2 \mid (n^2 − n)$ for $n\geq 1$
100375
Prove that ${\sqrt {n} }^{\sqrt {n+1}} > {\sqrt {n+1}}^{\sqrt {n}}$.
101899
Proof By Induction of a Sum
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Proof by Induction: $\sum_0^nx^i=(1-x^{n+1})/(1-x)$
156766
Prove that $\sqrt{\frac{n}{n+1}}\notin \mathbb{Q}$
134202
Proof by Induction - Math
39073
Proving that: $\forall n \in \mathbb{N} :|f^{(n)}(x)|\leq \frac{1}{n+1}$
86479
How to Prove with Mathematical Induction $3^n > n^2$
66996
Proof by induction of Bernoulli's inequality $ (1+x)^n \ge 1+nx$
87941
Prove by mathematical induction that $\forall n \in \mathbb{N} : \sum_{k=1}^{2n} \frac{(-1)^{k+1}}{k} = \sum_{k=n+1}^{2n} \frac{1}{k} $
67886
How to prove $\sum_{k=1}^{n}F_k = F_{n+2}-1$ by induction when $F_n$ is the Fibonacci sequence
115912
Summation inductional proof: $\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+\ldots+\frac{1}{n^2}<2$