sigma k=2 to infinity, 1/k^2-1

how do you break up the k^2-1 into a minus part? i cant do it theres no partial fraction form i can ffind? please help with a little bit (Rofl)

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- Jan 5th 2011, 05:00 AMmathcoretelescopic series
sigma k=2 to infinity, 1/k^2-1

how do you break up the k^2-1 into a minus part? i cant do it theres no partial fraction form i can ffind? please help with a little bit (Rofl) - Jan 5th 2011, 05:18 AMtonio
- Jan 5th 2011, 05:24 AMchisigma
Is...

(1)

... so that...

(2)

Kind regards

- Jan 5th 2011, 05:33 AMmathcore
how do you work out this part? how would you make that jump because i'm fine with the difference of two squares part but i couldnt reach the next part myself. the reason i ask how is because i dont wanna have to ask for the help for each question if i know the logic i can do my remaining questions just fine

thank you :) - Jan 5th 2011, 05:47 AMmathcore
also is 1/2 sigma (then the sum expression) the same as sigma 1/2 (then the sum expression). we were instructed to put the 1/2 to the left of the sigma, is this ok

- Jan 5th 2011, 05:58 AMLiverpool
using Partial Fractions Expansion.

and if c is a constant, then . - Jan 5th 2011, 06:00 AMmathcore
im stuck on another one:

it is sigma k=2 to infinity again, but the sum is 1/k^3-k

the reason i am stuck is the partial fracs give three parts then i dont know what to do

i solved it as -1/k + (1/2)/k+1 + (1/2)/k-1, i am lost because that doesnt really help me at all - Jan 5th 2011, 06:01 AMMiss
Do not put new problem in the same thread.

Post a new thread for the new one. - Jan 5th 2011, 06:06 AMmathcore
- Jan 5th 2011, 06:10 AMMiss
This is the rules of this forum.

If you post new problems in the same thread, It will be too hard to follow the replies.

Anyway, as a student taking infinite series, you should be able to find the partial fraction expansion.

You do not know how to find A,B & C ? - Jan 5th 2011, 06:48 AMmathcore
- Jan 5th 2011, 06:50 AMmathcore
what you have done there is exactly what i did but that form does not cancel out

- Jan 5th 2011, 06:52 AMmathcore
also i am not "taking infinite series", i did not say that. i did not even say i was a student. do not make these assumptions.

these are isolated problems that have not had any teaching hours dedicated to them - Jan 5th 2011, 06:55 AMGeneral
What is the statement of the problem?

You want to find its sum or just test its convergence? - Jan 5th 2011, 07:36 AMmathcore
find its sum

it is stated to be telescopic and as soon as i can see how the terms cancel out, i can find the sum, thats the easy part. but right now i cant see how to get them in a cancelling form