Thread: Sum of series

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!

Originally Posted by arze

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!

Try your partial fractions again.

Ok this is the way I worked it out:
For the part
When r=0, the other part of becomes
hence
then the next part, r=-1, and the part becomes
hence
hence we get the partial fraction
Is this correct?
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.

Even more simple...

(1)

... and now...

(2)

(3)

At this point You have to sum (2) and (3) toghether...

Kind regards

that's actually even easier.