find the taylor sum of sigma from 0 to infinity of ((-1)^n)(2)^(n +3)/(3^(2n + 1)(2n + 1) sorry i forget to add what was in bold. so that is the actual problem
find the taylor sum of sigma from 0 to infinity of ((-1)^n)(2)^(n +3)/(3^(2n + 1)(2n + 1) sorry i forget to add what was in bold. so that is the actual problem
If this is what you mean then
Then we can fix it up by rewriting it as
So we can identify this with the function
So now we can take the derivative to get
This is a geometric series so
So integrating we get
So now just evaluate this at
Last edited by TheEmptySet; May 3rd 2009 at 08:58 AM.
Reason: Typo Thanks Redsoxfan325 :)