# Series (Partial Sums )

1. Apr 3, 2009

### remaan

1. The problem statement, all variables and given/known data

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

2. Relevant equations

Finding the terms

3. 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 ??

2. Apr 3, 2009

### HallsofIvy

Staff Emeritus
If Sn= 1/(n+3)- 1/(n+1) then Sn+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?

3. Apr 3, 2009

### remaan

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

Last edited: Apr 3, 2009