I'm trying to figure out this problem and have no clue how to do it. The problem reads:

Use the identity 1/(k^2-1) = (1/2)(1/(k-1) - 1/(k+1)) to evaluate sum k=2 to n 1/(k^2-1)

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- Jun 8th 2009, 07:47 PMgeofflsummation problem
I'm trying to figure out this problem and have no clue how to do it. The problem reads:

Use the identity 1/(k^2-1) = (1/2)(1/(k-1) - 1/(k+1)) to evaluate sum k=2 to n 1/(k^2-1) - Jun 8th 2009, 07:57 PMKrizalid
the problem is almost solved, now, we have Then, if you consider does it telescope? what 'bout the other one?

- Jun 8th 2009, 08:00 PMgeoffl
what do you mean "does it telescope"? sorry, im new at this stuff.

- Jun 8th 2009, 09:00 PMmr fantastic
- Jun 8th 2009, 09:02 PMVonNemo19
What he means is that a telescoping sum is a sum that can be simplified by the cancelleling of terms through the addition that it implies.

e.g.

If you look carefully at this sum you can see that no matter how large n is that there will only be two terms left standing after what I call the addition wars. check it out

So after an uncountable number of n terms, who comes out of this war alive?

So now look at your problem with a trained eye. You have the ability to predict who's side you shoulb be on!(Bow) - Jun 8th 2009, 09:25 PMgeoffl
ahhh, ok. that makes sense.

thanks a lot!