Need some slight help on the following sum, this is my first post so i hope ive put this in the correct place
sum of from k=2 to infinity (1/(k^3-k)
currently i have the following, ive turned it to a partial fraction and obtained
sum of from k=2 to infinity (k/(k^2-1)-(1/k)
Then from this entering numerical values for k:
(2/3-1/2+3/8-1/3......) and so on however cant see any relation between numbers cancelling etc like in previous questions i have done.
Thanks in advance for any help.
1/2( 1/(k-1)-1/(k+1)-2/k) to get the series of 1/2(1-1/3-1+1/2-1/4/-2/3+1/3-1/5-1/2....) a lot of the terms cancel but cant see anything of such so not sure what to do....