Homework Help: Sum Series Explicit Formula

Andy111 · Apr 29, 2008

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 [tex]\frac{1}{2n(n+3)}[/tex]

2. Relevant equations

3. The attempt at a solution

rock.freak667 · Apr 29, 2008

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

tiny-tim · Apr 29, 2008

rock.freak667 said: ↑

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

That'll diverge, won't it?

Dick · Apr 29, 2008

tiny-tim said: ↑

That'll diverge, won't it?

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

HallsofIvy · Apr 29, 2008

tiny-tim said: ↑

That'll diverge, won't it?

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.

tiny-tim · Apr 29, 2008

HallsofIvy said: ↑

… 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.

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

thanks, HallsofIvy!