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

[c6_viyen_1995]

m > n >0

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

Thank you very much.

 

[TylerH]

You can't prove it, but you could solve for an m or n that describes the possible solutions.

 

[c6_viyen_1995]

Why that we can't prove it?

 

[TylerH]

You've got 2 variables and 1 statement.

 

[c6_viyen_1995]

oh, I couldn't understand!
Can you explain for me?
Thank you!

 

[TylerH]

I should've asked from the beginning, but what are you trying to prove? (1 + 1/m )^m > ( 1 + 1/n )^n is a statement. The only information you could get from that statement is the solutions to m in terms of n or solutions to n in terms of m.

 

[c6_viyen_1995]

y= (1 +1/x)^x
I want to know how to prove that : y' >0

 

[TylerH]

All you have to do is find the derivative of (1 + 1/x)^x.

 

[c6_viyen_1995]

oh!
could you help me to find the derivative of (1 + 1/x)^x ?

 

[TylerH]

I'll help. Show what you've got.

 

[c6_viyen_1995]

thank you very much.
I can't find derivative of (1 + 1/x)^x, so I haven't got anything...

 

[c6_viyen_1995]

oh... sorry
but I am not good at English subject. I couldn't find the word that I want to say.

 

[TylerH]

I'm not going to just give you the answer. There would be no good in that. There are sites that can find derivatives. http://www.wolframalpha.com/ is one of them.

 

[c6_viyen_1995]

Thank you for your advices!