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AP® Calculus AB-BC

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Moderate

Comparing Tests

APCALC-YLZDBK

Which of the following statements must be true if $\sum { { a }_{ n } } $ converges?

I. $\quad \lim _{ n\xrightarrow { } \infty }{ \left| \cfrac { { a }_{ n+1 } }{ { a }_{ n } } \right| } =0$

II. $\quad \lim _{ n\xrightarrow { } \infty }{ \sqrt [ n ]{ | { a }_{ n } | } } =1$

III. $\quad \lim _{ n\xrightarrow { } \infty }{ \left| \cfrac { { a }_{ n+1 } }{ { a }_{ n } } \right| } =\cfrac { 2 }{ 3 } $

A

I only.

B

I and II.

C

I and III.

D

I, II, and III.