Sum of Infinite Series: -3^(n-1)/(8^n) with Geometric Form and Scalar Value

[brusier]

Homework Statement

Find the sum of the following series.

SUM (n=1 to inf) -3^(n-1)/(8^n)

Homework Equations

Possibly fit into ar^n format?


3. The Attempt at a Solution [/b

I feel there is a way that this fits into a geometric form in which case could use a/(1-r) to find the infinite sum. I'm having trouble manipulating to fit into ar^n format when there are a couple powers of n in the general form.
Can the scalar 'a' value have an exponent in it? I guess not then it would be an exponential not a scalar

 

[ystael]

Your notation is ambiguous: do you mean $$\sum_{n=1}^\infty -\frac{3^{n-1}}{8^n}$$ or $$\sum_{n=1}^\infty \frac{(-3)^{n-1}}{8^n}$$ ?

Either way, you should try to find a way to split this fraction into $$\left(\frac{a}{b}\right) \cdot \left(\frac{c}{d}\right)^n$$. Then you will be able to apply the formula for the sum of a geometric series. You have the right idea; you just need to get the manipulations right.