Help in finding the sum of the series!
Find the sum of: -
A) (-2/3)^k when K goes from 1 to infinity...I got (3/5)!
B) 2^k / [3^(2k+1) when k goes from 0 to infinity...I got (9/7)!
c) 1 / k(k+1)...when K goes from 1 to infinity...I got (1)
d) 1 / k(k+2)...when K goes from 1 to infinity...I am not sure how to split this term in two different term.
I have got the solution for starting three, but I am not sure if I have done it right or not. I used the geometric series formula (1/1-r) in order to solve them.
Please help me making it sure!
Thanks!