- #1
The_Iceflash
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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.