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Suppose I have 2 seq, $a_n, b_n>0\forall n$ and a, b their limit respectively. If $c_n=\frac{a_n}{b_n}$ then it will converge if $b>0$ right? Is their any other condition for convergence of $c_n$?

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Yes, that is true. – M.B. Jun 2 '12 at 12:25

Notice by the limit laws we have:


if and only if $b\ne 0$.

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