Finding the Sum of a Series Using Partial Sums

[remaan]

Homework Statement

How to find the Sn of this patial sum : 1/n+3 - 1/ n+1 ??

Homework Equations

Finding the terms

The Attempt at a Solution

In fact, I tried finding s1 and s2 and so on till s6 and I found that the Sn is -1/ n+2 after I canceled the terms, is that right ??

 

[HallsofIvy]

If Sn= 1/(n+3)- 1/(n+1) then S_n+1= 1/(n+4)- 1/(n+2). Subtracting these two consecutive partial sums gives
$$]\frac{1}{n+4}- \frac{1}{n+2}- \frac{1}{n+3}+ \frac{1}{n+1}$$
What does that give you?

 

[remaan]

Are you trying to say that this method gives us Sn term directly, without a need for any subs. and finding terms ?