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Re: Analysis with series 1/2^2+1/3^2
Posted:
Aug 8, 2012 12:10 PM


On Wed, 8 Aug 2012 07:23:02 0700 (PDT), Mina <mina_world@hanmail.net> wrote:
>Hello teacher~ > >{(1/2^2) + (1/3^2) + (1/4^2) + ...} >+ {(1/2^3) + (1/3^3) + (1/4^3) + ...} >+ {(1/2^4) + (1/3^4) + (1/4^4) + ...} >+ ... > > >I have a solution.(ambiguous) > >Namely, > >{(1/2^2) + (1/3^2) + (1/4^2) + ...} >+ {(1/2^3) + (1/3^3) + (1/4^3) + ...} >+ {(1/2^4) + (1/3^4) + (1/4^4) + ...} >+ ... > >= > >(1/2^2 + 1/2^3 + 1/2^4 + ...) >+ (1/3^2 + 1/3^3 + 1/3^4 + ...) >+ (1/4^2 + 1/4^3 + 1/4^4 + ...) > >(this associative law ? Really possible?)
It's not just the associative law. But this manipulation is ok. The reason it's ok is because you're dealing with a sum of _positive_ terms; if you have a sum of positive terms any sort of regrouping or reordering is ok.
> >= > >(1/2^2)/{1(1/2)} >+ (1/3^2)/{1(1/3)} >+ (1/4^2)/{1(1/4)} >+... > >= (1/2) + (1/3).(1/2) + (1/4).(1/3) + ... > >= (1/2) + {(1/2)(1/3)} + {(1/3)(1/4)} + ... > >= 1 > > >Hm... how do you think about it ?



