What did this sum become: $\left(\sum_{n=a}^{b} z_n\right)^2 $? Can I see something meaningfull about this sum? Where is it equal to?
$$\left(\sum_{n=a}^{b} z_n\right)^2$$
Is it equal to: $\sum_{n=a^2}^{b^2} z_n^2$ or something else, I've no idea how to deal with it.
Thanks for the help.

$$\left(\sum_{n=a}^b z_n\right)^2 = \left(\sum_{j=a}^b z_j\right)\left(\sum_{k=a}^b z_k\right) = \sum_{j,k=a}^b z_jz_k$$
If you want, you can pull the squares and reduce repetitive terms into the following form:
$$\left(\sum_{n=a}^b z_n\right)^2 = \sum_{n=a}^b z_n^2 + 2\sum_{j=a+1}^b\left[\sum_{k=a}^{j-1} z_jz_k\right]$$
Unfortunately, there aren't many simplifications (in general) beyond this.  
