How to prove that geometric distributions converge to an exponential distribution? 
How to prove that geometric distributions converge to an exponential distribution?

To solve this, I am trying to define an indexing $n$/$m$ and to send $m$ to infinity, but I get zero, not some relevant distribution. What is the technique or approach one must use here?

I think we can just expand 1-p in Taylor series for small p we get the exponential function.:)
1-p=exp(-p) for very small p (around p=0)such that np=constant. so we find:
p(x)=(1-p)^x.p is becoming p exp(-px) for a continuous random variable x, this in part has the continuous exponential distribution function:)
