Series expansion

1. Apr 19, 2007

quasar987

1. The problem statement, all variables and given/known data
I am ashamed to ask this, but in my quantum final, there was a little mathematically-oriented subquestion that asked to show that the function

$$V(r)=-\frac{V_0}{1+e^{(r-R)/a}}$$

(r in [0,infty)) can be written for r>R as

$$V_0\sum_{n=1}^{\infty}(-1)^ne^{-n(r-R)/a}$$

3. The attempt at a solution

2. Apr 19, 2007

matt grime

You know the series expansion of (1+x)^-1 for |x|<1, right? So use it (and don't tell me that exp{(r-R)/a} >1 for r>R, because I know that).

3. Apr 19, 2007

quasar987

Yeah ok!

----

4. Apr 19, 2007

HallsofIvy

Staff Emeritus
Or (really the same thing) the "geometric series"
$$\sum_{n=0}^\infty ar^n= \frac{a}{1- r}$$