# Science:Infinite Series Module/Units/Unit 3/3.1 Power Series/3.1.01 A Motivating Problem for Power Series

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Earlier in the Infinite Series Module, we introduced the concept of a geometric series,

We assumed that *r* was a constant. But what if *r* were not a constant, and instead was a variable?

Let's replace our *r* with *x* in the above summation. We now obtain

From this simple substitution, we have created a **function**, and can ask two important questions related to this result.

## Key Questions for This Lesson

From our simple construction, we can ask:

- for what values of
*x*does our summation yield a finite result? - is there a more general representation of our summation?

The first question will take us to the idea of a **radius of convergence**, and the second question to the concept of a **power series**.