$\sum _{n=1}^{\infty }\:\left[\frac{2}{\left(n+1\right)}-\frac{2}{\left(n+3\right)}\right]$
This question is off from webwork and I already got everything right except for finding the nth partial sum. Here is what I have:
s3 = 1 + 2/3 - 2/5 - 2/6
s4 = 1 + 2/3 - 2/6 - 2/7
s5 = 1 + 2/3 - 2/7 - 2/8
It converges to 1 + 2/3
Now my nth partial sum is: 1 + 2/3 - 2/(n+1) - 2/(n+2)
But it seems to be incorrect. Can someone explain what I'm doing wrong?