
Re: Analysis with series 1/2^2+1/3^2
Posted:
Aug 9, 2012 12:17 PM


On Thu, 09 Aug 2012 13:47:18 +0100, Frederick Williams <freddywilliams@btinternet.com> wrote:
>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 ...?
Yes. Simply look at the partial sums. The sum of the first n terms on the left side _is_ 1  1/n (or 1  1/(n+1) or something), which tends to 1 as n tends to infinity.
But it's good to ask about this, because of the standard example
1 = 1 + (1+1) + (1+1) + ... = (11) + (11) + ... = 0.

