# mathematical induction

• Jun 7th 2007, 02:06 PM
Percent09
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.

• Jun 7th 2007, 02:13 PM
ThePerfectHacker
Quote:

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,
$x^n >1$
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