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Math Forum » Discussions » Math Topics » alt.math.undergrad.independent

Topic: Induction proof
Replies: 24   Last Post: Aug 22, 2006 4:11 PM

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emailtgs@gmail.com

Posts: 11
Registered: 8/17/06
Re: Induction proof
Posted: Aug 18, 2006 11:22 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Hi Torsten, thank you for your reply however you're solving a different
problem here. It appears that you've introduced a -1/n to the right of
the inequality for your convinience. That isn't the orignial problem.
I'm not sure what you're doing at all. Please everyone, here's the
problem ((((( 1/2^2 + 1/3^2 + ... + 1/n^2 < 1 ))))) FOR ALL n,
greater than or equal to 2, PROOF by INDUCTION. I only capitalized for
clarity, not yelling here.

Torsten Hennig wrote:
> >Prove by induction that 1/2^2 + 1/3^2 + ... + 1/n^2 < 1 >Please help!
> >Thank you!
>
> Hi,
>
> show by induction that
> 1/2^2 + 1/3^2 + ... + 1/n^2 < 1 - 1/n
> In the induction step, use that
> 1/(n+1)^2 < 1/(n*(n+1)) = 1/n - 1/(n+1) .
>
> Best wishes
> Torsten.

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