# How do I carry out an approximation for this equation?(if L Ns then what?)

1. May 6, 2012

### Raziel2701

$\frac{Ns-L}{L+Ns}$

What does that reduce to if L << Ns ? Obviously setting L to zero leads me nowhere since that argument above is actually inside a logarithm. I don't know how to perform the approximation. And the answer can't be zero by the way. Is there something I can do here? Usually the only approximations I've done before are just expansions but this is already expanded.

Thank you.

2. May 6, 2012

### AlephZero

You can write it as
$$\frac{1 - L/N_s}{1 + L/N_s}$$
and then use the Binomial theorem on $(1 + L/N_s)^{-1}$.