How Do You Solve a Complex Infinite Series?

[wilcofan3]

Homework Statement

$$\sum_1^{\infty} (1)/(n^3+n+4)$$

Homework Equations

I have only done problems where I've been finding whether the series converges or if I have been calculating, it's always been a factorable problem.

The Attempt at a Solution

Once again, I just need a few steps, I'm not asking anyone to solve it completely for me, but I would appreciate some sort of step-by-step breakdown of what to do. Thank you so much guys!

 

[quantumdude]

What are you supposed to do, find the sum or just determine if it converges?

 

[wilcofan3]

I'm supposed to calculate the sum correct to six decimal places.

Sorry about that, I was in a hurry to get it posted and forgot to actually put what the question wanted.

 

[Mark44]

It's easy to show by the comparison test that the series converges (compare with $\sum 1/n^3$).

For the approximate sum, just start adding terms in the series. When you get two successive partial sums that are the same in the first 6 decimal places, you're home free.