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neutralino · **Re: 0.999...=1 -** 02-14-2008, 07:44 PM

Quote:

Originally Posted by Profpat

Well I'm glad you started the thread Neutralino.

So are you concluding that infinity equals something finite?

No, I'm concluding that a sum of infinitely many terms can be equal to a finite number. Take the example I briefly mentioned in the shoutbox:
$\sum_{k+1}^{\infty}\frac{2}{k(k+1)}=1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\cdots$
$=2\left[\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\cdots \right]$
$=2\left[\left(1-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)+\cdots\right]$
$=2.$

So we see that a sum of infinitely many terms can indeed equal a finite number.