Question

Determine if the Summation from n=1 to infinity of (2n+3)/(5n+1) diverges or converges.

Answer 1

\[\sum_{n=1}^{\infty} \frac{ 2n+3 }{ 5n+1}\]

Answer 2

I think that \[\lim_{n \rightarrow \infty} \frac{ 2n+3}{5n+1 } = 2/5\]

Answer 3

According to the nth divergence test, if the limit of a as n goes to infinity does not equal 0, then the summation diverges.

Is this a solid argument?

Answer 4

Yes it is!