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AP® Calculus AB-BC

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Difficult

Challenging Convergence

APCALC-UVKWG4

Which of the following series converge?

I. $\sum_{n=0}^{\infty }\cfrac{1\cdot 3\cdot 5\cdots ( 2n-1 )}{2\cdot 5\cdot 8\cdots ( 3n-1 )} $

II. $\sum_{n=0}^{\infty }\left ( \cfrac{4n}{8n-1} \right )^{n} $

III. $\sum_{n=0}^{\infty }\cfrac{2^{n}}{3^{n}} $

A

I only.

B

II only.

C

I and III.

D

I, II, and III.