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mathematic problem

How to prove that for n > 2  
n to degree of n+1 is larger than (n+1) to degree of n
1
user_n
Asked:
user_n
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1 Solution
 
phoffricCommented:
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
0
 
user_nAuthor Commented:
Thank you very much
0
 
phoffricCommented:
You're welcome
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