Explicit Formula for Sum of Series with Fractional Terms

[Andy111]

Homework Statement

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

Homework Equations

The Attempt at a Solution

 

[rock.freak667]

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

 

[tiny-tim]

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

That'll diverge, won't it?

 

[Dick]

That'll diverge, won't it?

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

 

[HallsofIvy]

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]

… 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!