# Rewritting sum as hyperbolic sine

1. Oct 24, 2008

### jorgen

Hi all,

I have to rewrite a serie into a fraction of hyperbolic sine but I am lost.... My problem looks like this

$$\Sigma_{n=0}^{\infty} exp(K*F)*exp(-F*B(n+0.5))$$

which can be rearranged into

$$exp(K*F)/(sinh(FB/2)$$

my problem is I cannot relate the serie

$$\Sigma_{n=0}^{\infty}exp(-F*B(n+0.5))$$

Best
Jorgen
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Oct 24, 2008

### Dick

Take the 0.5 part out, so you have e^(FK)*e^(-FB/2)*e^(-FBn). You want the sum over n of e^(-FBn). That's the same as (e^(-FB))^n. It's a geometric series.