Math Is Fun Forum

c6_viyen_1995

Member

Registered: 2011-03-20

Posts: 1

(1 + 1/m )^m > ( 1 + 1/n )^n

m > n >0

How can prove that (1 + 1/m )^m > ( 1 + 1/n )^n ?

Thank you very much.

123ronnie321

Member

Registered: 2010-09-28

Posts: 128

Re: (1 + 1/m )^m > ( 1 + 1/n )^n

Hi c6_viyen_1995,

Graph this function y = (1+1/x)^(x) here http://www.mathsisfun.com/data/grapher-equation.html.
It is always increasing in (0,∞). You can prove this using calculus.
Post again if you have any problem.