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# Limit Comparison

APCALC-CEB2DB

Given ${ a }_{ n }>0$ and ${ b }_{ n }>0$ for all values of $n$.

If $\sum { { a }_{ n } }$ converges and

$$\displaystyle\lim_{n \to \infty }\cfrac{a_{n}}{b_{n}}=3$$

...which of the following must be true?

A

$\sum { { b }_{ n } }$ converges

B

$\sum { { b }_{ n } }$ diverges

C

$\sum { { a }_{ n } } = \sum { { b }_{ n } }$

D

$\sum { { a }_{ n } } <\sum { { b }_{ n } }$