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Analysis with series 1/2^2+1/3^2
Posted:
Aug 8, 2012 10:23 AM


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?)
=
(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 ?



