limit of $\frac{F(c_n)}{F(d_n)}$,where $\frac{c_n}{d_n} \to 1$ as $n\to\infty$ Suppose F(continuous) is the cdf of a non-negative random variable, and $c_n$,$d_n$ are two positive sequences going to zero as n$ \to \infty$, such that $\frac{c_n}{d_n}\to 1$. Can it be said that $\frac{F(c_n)}{F(d_n)}$ also goes to 1? Are there any additional assumptions which could make this statement true?

It seems that there is no general way of answering this question without further information. One assumption which makes this statement true(which I have mentioned in reply to RSerrao's comment) is $F^{1}(0)>0$.In that case we can write $\frac{F(c_n)}{F(d_n)}$ as $\frac{F(c_n)}{c_n}$*$\frac{d_n}{F(d_n)}$*$\frac{c_n}{d_n}$and take limits.
