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

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Torsten Hennig

Posts: 2,419
Registered: 12/6/04
Re: Induction proof
Posted: Aug 18, 2006 2:32 AM
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>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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