Alternating Series and Absolute Convergence

Question

First find the partial fraction decomposition of 3/k(k+6) = 0.5/k - 0.5/k+6

Then find the limit of the partial sums = .......

Enter your answer for the sum as a reduced fraction.

Hint: The alternating series is a telescoping series. Write down its terms using the partial fraction decomposition until some terms cancel.

I am not sure what to do for the second part of the question.

Answer 1

First, I assume you want the infinite series beginning at k-1.

Since all the terms are positive and the series converges , it converges absolutely.

There is no alternating term series as you have submitted the problem.

Only the first 6 terms are relevant: (1/2)[1+(1/2)+...+(1/6)]