1. ## series and sequences

let an=2n/(3n^2+2)
a.)determine whether the sequence {an}n=1-infinity is convergent or divergent. If it converges find the limit
b.)determine whether the series sum from n=1 to infinity of an is convergent or divergent.

Can someone explain to me how to do this i am completely confused on series and apparently this is an easy workout problem. Help please? Thanks!

2. Originally Posted by ahawk1
let an=2n/(3n^2+2)
a.)determine whether the sequence {an}n=1-infinity is convergent or divergent. If it converges find the limit
b.)determine whether the series sum from n=1 to infinity of an is convergent or divergent.

Can someone explain to me how to do this i am completely confused on series and apparently this is an easy workout problem. Help please? Thanks!

A sequence converges if it has a limit as n->infinity, and diverges if the limit DNE or is infinity.

4. For the limit of the series, note that $\displaystyle 4n^2 > 3n^2 + 2$ for $\displaystyle n \geq 2$. Hence, $\displaystyle \frac{2n}{3n^2 + 2} > \frac{2n}{4n^2}$ for $\displaystyle n \geq 2$. But $\displaystyle \frac{2n}{4n^2} = \frac{1}{2n}$ which is a multiple of the harmonic series. What can you conclude from this?