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Thread: mathematical induction

  1. #1
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    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.

    Thanks in advance
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  2. #2
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    Quote Originally Posted by Percent09 View Post
    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.

    Thanks in advance
    You do not need induction.

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

    Multiply them,
    $\displaystyle ac>bd>0$

    So,
    $\displaystyle x>1$
    $\displaystyle x>1$
    ....
    $\displaystyle x>1$

    Multiply them out,
    $\displaystyle x^n >1$
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