Eugene E. answered • 10/12/15

Calculus Tutor near downtown Naperville

_{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).
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Tumaiesla G.

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