Math Is Fun Forum

LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

How to prove Bernoulli's inequality using Induction?

Prove that if h>-1 then 1+nh <= (1+h)^n

So I did the basis step:

Inductive step:

So:

But I got stuck and dont know how to continue...I dont know how to keep filling the blanks so the induction is finished. Could anyone help me?

Last edited by LuisRodg (2008-03-28 03:44:31)

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: How to prove Bernoulli's inequality using Induction?

which is true for all h, and for all k>=0. since we started with k=1. we don't have to worry about that.

hence:

Hope i didn't make a mistake

Last edited by luca-deltodesco (2008-03-28 03:56:18)

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LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Re: How to prove Bernoulli's inequality using Induction?

Thanks a lot luca. I understand it now. I didnt reply sooner because I had to run to take my test but as I mention in another topic, it was canceled.

Thanks a lot.