# Finding the divergence or convergence of a series

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?

LCKurtz
Homework Helper
Gold Member
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)?

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

LCKurtz
Homework Helper
Gold Member
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

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?

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

LCKurtz