# Sum Series Explicit Formula

1. Apr 29, 2008

### Andy111

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

Find an explicit formula for the sum of the series, given that the formula for any term in the series is $$\frac{1}{2n(n+3)}$$

2. Relevant equations

3. The attempt at a solution

2. Apr 29, 2008

### rock.freak667

Try splitting it into partial fractions and see if that takes you anywhere.

3. Apr 29, 2008

### tiny-tim

That'll diverge, won't it?

4. Apr 29, 2008

### Dick

It's similar to 1/n^2. That's a p series with p=2. It converges.

5. Apr 29, 2008

### HallsofIvy

Staff Emeritus
I'm not sure what you mean by that, since you said this, not in response to the initial post, but in response to the suggestion to use partial fractions to split it into to parts.

Perhaps you meant that the two parts would each diverge separately. But that's not the point- you don't want to look at them separately- you want to see if there are terms at one point that will cancel terms at another point. In fact, partial fractions works nicely.

6. Apr 29, 2008

### tiny-tim

oh yes … so it does … isn't that nice!

thanks, HallsofIvy!