Series Expansion

Question

Find the series expansion of ln(1+e^(-z)) when z is very large.

I figured this out for when z is very small but I am unsure what to do if z is very large. I think if I just get a hint about that I can figure the rest out.

Answer 1

Hint: When $z$ is very large, the exponential $e^{-z}$ is close to $0$, hence you can use the Taylor expansion of $\log(1 + x)$ when $x$ is near $0$.