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AP® Calculus AB-BC

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Direct Comparison Test

APCALC-SLVLDY

$\sum { { a }_{ n } } $ and $\sum { { b }_{ n } } $ are series with all positive terms.

If $0 \leq a_n \leq b_n $for all $n$, which of the following statements must be true?

I.$\ \text{If}\ \sum { { b }_{ n } } \ \text{converges, then}\ \sum { { a }_{ n } } \ \text{converges.}$
II.$\ \text{If}\ \sum { { a }_{ n } } \ \text{diverges, then}\ \sum { { b }_{ n } } \ \text{diverges.}$
III.$\ \text{If}\ \sum { { b }_{ n } } \ \text{diverges, then}\ \sum { { a }_{ n } } \ \text{diverges.}$

A

I only.

B

II only.

C

III only.

D

Iand II.