Math Is Fun Forum

hypatia

Member

Registered: 2010-07-10

Posts: 1

Proving an inequality

Dear all,

i'm struggling to find a way to show that

holds for all integers

and

.

Could anybody help me out with a hint on how to proceed?
Thanks a lot!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Proving an inequality

Hi hypatia;

So far I haven't been able to algebraically manipulate your inequality so that it is obviously true. Maybe you can apply induction?

Download this pdf on induction;

http://www.mathdb.org/notes_download/el … /ae_A2.pdf

It appears now that you have two strategies ,one is to relax the condition on either k or n of being an integer and defining one of them as Real. Then you can do a single dimensional induction on the other variable.

Or you can use what is on page 12 of the pdf as induction with 2 variables.

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