# Factorials approximation problem

1. Feb 25, 2008

### karnten07

1. The problem statement, all variables and given/known data
How is,

[(N+Q)!Q!]/[(Q+1)!(N+Q-1)!] equal to (N+Q)/(Q+1) when N,Q>>1 ??

It looks like the Q!/(N+Q-1)! cancels but i don't see how, im going from my lecturers notes here.
2. Relevant equations

3. The attempt at a solution

Last edited: Feb 25, 2008
2. Feb 25, 2008

### TheoMcCloskey

Break it up - look at the fraction as

$$\frac{Q!}{(Q+1)!} \cdot \frac{(N+Q)!}{(N+Q-1)!}$$

For the first fraction, ask yourself "what number you would multiply $Q!$ by to get $(Q+1)!$"?

Do a similar analysis for the second fraction.