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Phil H
Posts:
49
Registered:
4/13/10


Re: Analysis with series 1/2^2+1/3^2
Posted:
Aug 8, 2012 6:27 PM


On Wednesday, August 8, 2012 7:23:02 AM UTC7, Mina 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?) = (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 ?
Any series can be fluffed out to make it more challenging. Unfluffed, this one is 1/(n^2+n)........1/2 + 1/6 + 1/12 + 1/20...... = 1/2 + (1/2  1/3) + (1/3  1/4) + (1/4  1/5) ...... = 1 Phil H



