Geometric series. Find the sum of the series. Powers.

[NotaPhysicist]

Homework Statement

Find the sum of 9 terms of the series 3 + 3^(4/3) + 3^(5/3) + ...

Homework Equations

I'm just learning sequences and series and senior high school level. I'm finding it hard to apply a, ar, ar^(n-1), ... to this.

a = 3.

I don't know how to find common ratio. I'm confused. Once I know r I can apply the standard formula for summing the series.

The Attempt at a Solution

Any help will be greatly appreciated.

 

[VietDao29]

Homework Statement

Find the sum of 9 terms of the series 3 + 3^(4/3) + 3^(5/3) + ...

Homework Equations

I'm just learning sequences and series and senior high school level. I'm finding it hard to apply a, ar, ar^(n-1), ... to this.

a = 3.

I don't know how to find common ratio. I'm confused. Once I know r I can apply the standard formula for summing the series.

The Attempt at a Solution

Homework Statement

Homework Equations

The Attempt at a Solution

Any help will be greatly appreciated.

In geometric series, the following term is obtained by multiplying the previous term by the common ratio r. Which, in turn, means that, you can obtain r by dividing the following term by the previous term; like this:

$$r = \frac{a_2}{a_1} = \frac{a_3}{a_2} = ... = \frac{a_n}{a_{n - 1}}$$

So, can you calculate the common ratio in the problem above?

 

[NotaPhysicist]

Yes! I got it now. Thanks for your help!