Rewritting sum as hyperbolic sine

[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

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

any hints or advice appreciated.

Thanks in advance

Best
Jorgen

 

[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.