By expressing the rth term of the series in partial fractions, or otherwise, find the sum of the series.
If this sum is denoted by prove that for all odd values of n,
I found the partial fractions to be:
and the sum of the series:
but the sum is given as
Thanks!
No, the partial fraction decomposition is
[LaTeX ERROR: Convert failed]
Also here's how to get it
[LaTeX ERROR: Convert failed]
So you have [LaTeX ERROR: Convert failed] is valid for all r, so let
r = 0, you get A = 1
r = -1/2, you get A/2-B/2 = 0 which implies A = B
Thus you get your result.
Then just multiply the result by (-1)^{r+1} and then just do your sum.