Question

Find the sum of the series. from n=1 to infinity. 6/(2n-1)(2n+1)

Answer 1

You can try breaking up your fraction using partial fractions.. I'm assuming you mean \[\frac{6}{(2n-1)(2n+1)}\]

Answer 2

^ yes, sorrry first time using this. didn't know how to write it. but I tried removing the 6 and doing a comparison with.\[1/n^2\] and then
\[\lim_{n \rightarrow \infty } \frac{ 1 }{ 4n^2-1}\frac{ n^2 }{ 1 }\]

Answer 3

You can do a comparison test here, but it will only tell you if it's convergent or divergent and the the value of the actual sum. The way the question is worded already implies that the series is convergent (since you're asked to find it's sum), so it's not necessary to do this step.

If you break the fraction using partial fractions, you will see that you get some sort of telescoping series (by plugging in values for n=1, n=2, n=3.. and you should see a pattern emerge).

Answer 4

it will only tell you if it's convergent or divergent and not** the value of the actual sum.

Answer 5

Thank you! I did realize it converged to 1.

Answer 6

np :)