1. ## mathematical induction

Hello, I was wondering if anyone can help

If x > 1, prove by inducction that x^n > x for every integer n >= 2 . If
0<x<1, prove that x^n < x for every integer n>= 2.

2. Originally Posted by Percent09
Hello, I was wondering if anyone can help

If x > 1, prove by inducction that x^n > x for every integer n >= 2 . If
0<x<1, prove that x^n < x for every integer n>= 2.

You do not need induction.

Just use the rule that if,
$a>b>0$
$c>d>0$

Multiply them,
$ac>bd>0$

So,
$x>1$
$x>1$
....
$x>1$

Multiply them out,
$x^n >1$