# Finding the divergence or convergence of a series

1. Nov 27, 2011

### aimsanko

Ʃ ,n=1,∞, (2/n^2+n)

Does this series converge or diverge?

Im not sure how to start can i use the comparison test here?

2. Nov 27, 2011

### LCKurtz

You can begin by making sure you stated the problem you meant to state. Is that expression (2/n2)+n, which is what you wrote would mean, or 2/( n2+n)?

3. Nov 27, 2011

### aimsanko

its 2/((n^2)+n)
and I'm thinking it converges because you are adding an infinite amount of numbers that are continually getting smaller and smaller

4. Nov 27, 2011

### LCKurtz

Both convergent and divergent series have an infinite number of terms that get smaller and smaller, so that observation is of no value. For example, do you know the p series
$$\sum \frac 1 {n^p}$$
and for what values of p it converges or diverges?

Do you know how to use the comparison tests? What might you compare your series with and why?

5. Nov 27, 2011

### aimsanko

if p is greater than 1 the series converges
im not very good at the comparison test and how to find what to cop are it to

6. Nov 27, 2011

### LCKurtz

The first step in a comparison test is to decide by examining your series whether you think it probably converges or diverges. This is usually decided by previous experience with previously analyzed series such as a p series. The next step depends on your expectation of convergence or divergence.

If you think your series might converge, try to find a larger series that you know does converge. Then you have a series smaller than a known convergent series so it converges.

If you think your series might diverge, see if you can find a smaller series that you know diverges. If your series if larger than a known divergent series, it must diverge.

Your problem has similarities to a p series about which you know convergence or divergence. So think about that.