# Thread: Series Problem

1. ## Series Problem

Problem:

Consider the following infinite series.

$\displaystyle 3 - 3x + 3x^2 - 3x^3 + 3x^4 - ...$

(a) For what values of x will the sum of the series be a finite value?
(b) Find the value of the infinite series for x in the interval in part (a).

Could somebody explain how this is done? I really don't understand where to even start...

2. Originally Posted by lysserloo
Problem:

Consider the following infinite series.

$\displaystyle 3 - 3x + 3x^2 - 3x^3 + 3x^4 - ...$

(a) For what values of x will the sum of the series be a finite value?
(b) Find the value of the infinite series for x in the interval in part (a).

Could somebody explain how this is done? I really don't understand where to even start...
It is a geometric series.

3. I understand that, but I don't understand how to find the sum when x has to be in an interval from -1 to 1 (the answer to part a).

How do I solve when x is an interval and not a set number?

4. Originally Posted by lysserloo
I understand that, but I don't understand how to find the sum when x has to be in an interval from -1 to 1 (the answer to part a).

How do I solve when x is an interval and not a set number?
You should know then that a = 3 and r = -x. Now, what is the condition on r for an inifinite geometric series to have a finite value ....?