# Math Help - sequences

1. ## sequences

how does one tell if an= 2n/(3n+1) is convergent?

i think i remember my instructor saying that you can't just use the coefficients of the highest degrees of n.. but i missed this lesson

also, upon deciding whether or not that is convergent, how do you decide if the series from n=1 to infinity is convergent?

2. For sequences, if $\lim_{n \to \infty} a_n$ exists, then it is convergent.

For series, there are a lot of tests that you can use to determine whether or not $\sum a_n$ is convergent.

For this particular example, we have the divergent test which says: If $\lim_{n \to \infty} a_n \neq 0$, then $\sum a_n$ is divergent.