I need to come up with a proof to this problem but it's giving me a hard time...

Show that if $\displaystyle lim \frac{a_{n}}{b_{n}}$ converges and $\displaystyle \sum b_{n}$ converges, then $\displaystyle \sum a_{n}$ converges.

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- Apr 28th 2012, 09:45 PMjameselmore91Problem Regarding Convergent Series.
I need to come up with a proof to this problem but it's giving me a hard time...

Show that if $\displaystyle lim \frac{a_{n}}{b_{n}}$ converges and $\displaystyle \sum b_{n}$ converges, then $\displaystyle \sum a_{n}$ converges.