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If sequence$\frac{A}{B}\rightarrow \alpha\neq 0$, show if A is summable, B is summable.

I was trying to use contrapositive of the statement suppsoe A converges to L and B to M.$If M\neq 0 then \frac{A}{B}\rightarrow \frac{L}{M}$

But it didn't work out well since we do not know if B has a limit or not. How do I show B converges?

Kun
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  • I don't think the problem statement makes sense. Where did the problem come from? – Jonas Meyer Oct 10 '14 at 01:34
  • Why doesn't it make sense. I mean B could also go to zero so it will make sense. But I just try to prove B converges first. Then use contradiction to show that B has to go to zero. – Kun Oct 10 '14 at 01:36
  • I just changed the problem .... sorry – Kun Oct 10 '14 at 01:38

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