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## Homework Statement

Given [tex]\lim_{n\rightarrow \infty}a_{n}}= 0[/tex]

[tex]b_{n}[/tex] is bounded below.

Prove: [tex]\lim_{n\rightarrow \infty}(a_{n}+b_{n})}= \infty[/tex]

## Homework Equations

N/A

## The Attempt at a Solution

According to my text: [tex]{b_{n}}[/tex] is bounded below if and only if there is a real number [tex]\ni[/tex] B [tex]\leq[/tex] [tex]b_{n}\forall_{n}[/tex]

So, here's my attempt:

Putting the givens together I get:

B [tex]\leq[/tex] [tex]b_{n}[/tex] [tex]\leq[/tex] 0

At this point forward I'm not sure where to go with this. Any kind of help is appreciated.