mathematic problem

Posted on 2013-05-15
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Last Modified: 2013-05-15
How to prove that for n > 2  
n to degree of n+1 is larger than (n+1) to degree of n
Question by:user_n
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Accepted Solution

phoffric earned 500 total points
ID: 39167793
If n^(n+1) > (n+1)^n
then by dividing RHS ==>
n^(n+1) / (n+1)^n > 1 ==>
n * n^n / (n+1)^n > 1 ==>
n * [ n/(n+1)]^n > 1 ==>
n * [1/(1+1/n)]^n  > 1 ==>
n / (1 + 1/n)^n > 1
and for n > 2, then (1+1/n) < 2
so it is true that n / (1 + 1/n)^n > 1

Working backwards with this last fact, you find that n^(n+1) > (n+1)^n

Author Comment

ID: 39167836
Thank you very much
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Expert Comment

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