What is the thing on the left side of a sum mean?

Question

To be more specific:

What is the thing on the left side of a sum mean?

Answer 1

So, $|N|$ means the number of elements in $N$. And if we write in for example $$ c\sum_i a_i x^i, $$ what we mean is $$ c\cdot \left(\sum_i a_i x^i\right). $$ That is to say, "stuff on the left side of a sum" is not connected to the sum at all; we just multiply the whole sum by it.

(^ Some of that might be obvious to you; in that case don't take it as patronising or anything, I just don't know where you're coming from.)