Does this series have an analytical solution?

[FrankDrebon]

Hi all,

Can anyone show how I'd work out the analytical solution to an infinite series of this form:

$$\sum\limits_{n = 0}^\infty {\exp \left( { - An} \right)}$$

Thanks in advance,

F

 

[uart]

Hi all,

Can anyone show how I'd work out the analytical solution to an infinite series of this form:

$$\sum\limits_{n = 0}^\infty {\exp \left( { - An} \right)}$$

Thanks in advance,

F

It's just a geometric series Frank

$$\sum\limits_{n = 0}^\infty {\exp \left( { - An} \right)} = \frac{1}{1 - e^{-A}}$$

Converges for A>0

 

[arildno]

Just to fill in a detail:
$$e^{-An}=(e^{-A})^{n}$$
For all A and n.

As uart said, this is a geometric series.