# Very brief summnation question

1. Dec 2, 2014

If there is a sum:
i=1, and ends at N

Why, if there is an N, is it considered as a constant.
As opposed to an i inside of a summnation.

I would understand that if for example, there were a Z, Q,E, or W, it's a non-variable.
But N, that's ON top of the sum!
Wouldn't it.. like turn into soemthing? Can anyone explain thoroughly?

2. Dec 3, 2014

### Stephen Tashi

Whether a symbol is a constant depends on the full context surrounding it's use. In the majority of typical textbook problems and discussions the $N$ in an expression like $\sum_{i=1}^N a_i$ represents a constant. But there is no absolute rule that $N$ must be used that way. For example, a person could say "Consider the function $F(N) = \sum_{i=1}^N (2i^2 + 6)$", using $N$ as a variable.