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Re: Analysis with series 1/2^2+1/3^2
Posted:
Aug 8, 2012 12:24 PM


Hello Mina 
Am 08.08.2012 16:23 schrieb Mina: > 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,
I append the "zeta"expression at each row:
> > {(1/2^2) + (1/3^2) + (1/4^2) + ...} \\ = zeta(2)  1 > + {(1/2^3) + (1/3^3) + (1/4^3) + ...} \\ = zeta(3)  1 > + {(1/2^4) + (1/3^4) + (1/4^4) + ...} \\ = zeta(4)  1 > + ... > because everything is convergent, you can reorder to get your sums of geometric series.
It is also known, that oo Sum (zeta(k)1) = 1 k=2
(zeta(k)1) converges very fast to zero with increasing k.
Gottfried Helms



