Proving a positive series converges

[missavvy]

Homework Statement

Let {a_n}_n≥1 and {b_n}_n≥1 be strictly positive series.
If the limit n-> infinity (a_n/b_n) = c /= 0, then the \sum a_n converges iff \sum b_n converges, n≥1

Homework Equations

The Attempt at a Solution

Since we know that lim (a_n/b_n) = c, then
for all ε>0, \exists a natural number N s/t for all n≥N,
|a_n/b_n - c| < ε.

Then suppose the \sum a_n converges but the \sum b_n does not...

I'm trying to understand what to prove exactly.. so IF the limit of (a_n/b_n) = c, THEN the 2 series converge.. but it's confusing me since there is the second iff... what do I prove first?
Also any advice on how to go about it?

 

[hunt_mat]

You know that the is an N such that:
<br /> \frac{a_{n}}{b_{n}}-c&lt;1<br />
Hence
<br /> a_{n}&lt;(c+1)b_{n}<br />
What now?

 

[missavvy]

Should I use comparison?

 

[micromass]

Yes, comparison is good.