I need to find the sum:
sigma 0-->infinity (-1/3)^n * 1/(2n+1)
i looked at the power series : x^2n (1)
the sum of this series is : 1/(1-x^2) (2)
then by integration of (1) I got : x^2n+1 * 1/(2n+1) (3)
by integration of (2) i got the sum of (3)
I dont know what to do now
help would be appreciated.