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AP® Calculus AB-BC

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Moderate

Convergent Sequences

APCALC-JJJDVO

Which of the following sequences converge?

$$I. a_{n}=\left \{ \frac{2n}{3n+5} \right \}$$
$$II. b_{n}=\left \{ \frac{e^{n}}{n^{2}} \right \}$$
$$III. c_{n}=\left \{ \frac{3^{n}}{n!} \right \}$$

A

$I$ only

B

$III$ only

C

$I, II$ and $III$

D

$I$ and $III$ only