Use Induction to prove that for all $n \in \mathbb{N}, (x^n + \frac{1}{x^n}) \in \mathbb{Z}$ if $x+\frac{1}{x}\in\mathbb{Z}$.
36906
Prove that $x^n+x^{-n} \in \mathbf{N}$ if $x+\frac1x \in \mathbf{N}$
62613
Need to proof by induction (calculus1 n and n+1)
61117
Prove by induction: $n! \ge 2^{(n-1)}$ for any $n \ge 1$
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} $
90789
Use induction to prove that that $8^{n} | (4n)!$ for all positive integers $n$
102738
Show that $e^n>\frac{(n+1)^n}{n!}$ without using induction.
95000
Using induction to prove that $2 \mid (n^2 − n)$ for $n\geq 1$
15838
Induction Proof that $x^n-y^n=(x-y)(x^{n-1}+x^{n-2}y+\ldots+xy^{n-2}+y^{n-1})$
62556
Prove $3|n(n+1)(n+2)$ by induction
121107
Proof by induction: $n^{n+1} > (n + 1)^n$, $(1 + x)^n \ge 1 + nx$, other inequalities
119436
Proving $2^n\leq 2^{n+1}-2^{n-1}-1$ for all $n\geq 1$ by induction
148330
Induction Proof for $F_{2n} = F^2_{n+1} - F^2_{n-1}$
86479
How to Prove with Mathematical Induction $3^n > n^2$
108596
Proof by induction for "sum-of"
78583
Help with proof using induction: $1 + \frac{1}{4} + \frac{1}{9}+\cdots+\frac{1}{n^2}\leq 2-\frac{1}{n}$
71650
Proving by strong induction for a sequence of integers, $2^n$ divides term $n$
100080
Proving with induction $(1-x)^n<\frac 1 {1+nx}$