Question

Prove that if x+ \frac{1}{x} is integer then x^n+ \frac{1}{x^n} is also integer for any positive integer n.

KEY NOTE: PROVE BY INDUCTION

Answer #1

$\frac{1}{0!}+\frac{1}{1!}+\frac{1}{2!}+....+\frac{1}{n!}<3-\frac{2}{(n+1)!}$\
$\forall\in\mathbb{N}$ / {1} proof by induction

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