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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Analysis with series 1/2^2+1/3^2
Replies: 8   Last Post: Aug 9, 2012 12:17 PM

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Frederick Williams

Posts: 2,166
Registered: 10/4/10
Re: Analysis with series 1/2^2+1/3^2
Posted: Aug 9, 2012 8:47 AM
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pholman50@gmail.com wrote:

> 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

May one rearrange 1/2 + (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) ... to
get (1/2 + 1/2) + (- 1/3 + 1/3) + (- 1/4 + 1/4) + - 1/5 ...?

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