# plz can someone help me to proof this

#### majed

Dear all

I need your help I want to proov the follwing

#### chiro

MHF Helper
Hey majed.

Can you please show us what you have tried?

#### Archie

You should start by noticing that you have
$$\displaystyle \sum_{n=-J}^{J} \mathrm e^{nx \over J} = 1 + \sum_{n=1}^J \mathrm e^{-{nx \over J}} + \mathrm e^{nx \over J} = 1 + \sum_{n=1}^J 2\cosh{nx \over J}$$​
I would then multiply this by $$\displaystyle \sinh{x \over 2J}$$ and use product-sum identities to simplify.

Why do so many people use such needlessly complicated notation on here? What is $$\displaystyle m_j$$ all about?

1 person