Question

Do I just use telescoping method to find the sum of the series

\[\sum_{n=1}^{\infty}-3/n(n+4)\]

Answer 1

Is that \[\sum_{n=1}^\infty \frac{-3}{n(n+4)}?\]

Answer 2

yes how do you do that in latex btw

Answer 3

\sum_{n=1}^\infty \frac{-3}{n(n+4)}

Answer 4

thanks, would I use telescoping method, where I use partial fractions then cancel terms and then take the limit

Answer 5

That seems like it would work well.

Answer 6

By taking the limit do I receive the sum of the function?

Answer 7

No. If you take the limit, you get 0, but the sum is not 0.

Answer 8

right but if I take the limit of the terms that cancel out after using partial fractions

Answer 9

After using partial fractions, you'll get some terms in the beginning that don't cancel. Add these together. Then take the limit of partial sum expansion. Add the limit, and any other terms at the end that don't entirely cancel.

Answer 10

right and that will give me the sum right :)

Answer 11

Right. Feel free to post any work here and I can check it.

Answer 12

ok thanks

Answer 13

also would you mind checking this I determine the series was convergent based on the comparison test



where the series 1/r^(p) is convergent when p>1 therefore by C.T. the original series is converget