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

In summary, the student is struggling with finding the sum of a geometric series and is unsure of how to apply the formula for finding the sum. They are looking for help in finding the common ratio, which can be calculated by dividing the following term by the previous one. With this understanding, they are able to solve the problem.
  • #1
NotaPhysicist
25
0

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.
 
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  • #2
NotaPhysicist said:

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:

[tex]r = \frac{a_2}{a_1} = \frac{a_3}{a_2} = ... = \frac{a_n}{a_{n - 1}}[/tex]

So, can you calculate the common ratio in the problem above?
 
  • #3
Yes! I got it now. Thanks for your help!
 

What is a geometric series?

A geometric series is a sequence of numbers where each term is found by multiplying the previous term by a constant ratio. For example, the series 1, 2, 4, 8, 16, ... is a geometric series with a common ratio of 2.

How can I find the sum of a geometric series?

The sum of a geometric series can be found using the formula S = a/(1-r), where S is the sum, a is the first term, and r is the common ratio. Alternatively, the sum can also be found by multiplying the first term by (1-r^n)/(1-r), where n is the number of terms in the series.

What is the formula for finding the sum of an infinite geometric series?

The formula for finding the sum of an infinite geometric series is S = a/(1-r), where S is the sum, a is the first term, and r is the common ratio. This formula only works if the absolute value of r is less than 1.

Can the sum of a geometric series be negative?

Yes, the sum of a geometric series can be negative. This can occur if the common ratio is a negative number and the number of terms in the series is odd.

What is the significance of powers in a geometric series?

The powers in a geometric series represent the exponent of the common ratio. They increase by 1 with each term in the series, and determine the pattern of growth or decay in the series. Additionally, the powers are used in the formula for finding the sum of a geometric series.

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