_{n}converges, then lim a

_{n}=0. With a

_{n}= n

^{2}/(5n

^{2}+4), we have lim a

_{n}= 1/5 ≠ 0. So by the nth term test, your series diverges.

Eugene E.

tutor

It's lim a

_{n }= 1/5, since a_{n }can be written 1/(5 + 4/n^{2}), and lim 4/n^{2 }= 0 (which implies lim a_{n}= 1/(5 + 0) = 1/5).
Report

10/12/15

Tumaiesla G.

_{n}_{?}10/12/15