Why Is N Considered a Constant in Summation Notation?

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SUMMARY

In summation notation, the variable N is typically treated as a constant, particularly in standard textbook problems, where it defines the upper limit of the summation, such as in the expression ∑i=1N ai. However, the context can dictate its usage; for instance, in the function F(N) = ∑i=1N (2i² + 6), N is utilized as a variable. This highlights that while N is often a constant in summation, it can also represent a variable depending on the mathematical context.

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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?
 
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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 [itex]N[/itex] in an expression like [itex]\sum_{i=1}^N a_i[/itex] represents a constant. But there is no absolute rule that [itex]N[/itex] must be used that way. For example, a person could say "Consider the function [itex]F(N) = \sum_{i=1}^N (2i^2 + 6)[/itex]", using [itex]N[/itex] as a variable.
 

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