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

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SUMMARY

The discussion focuses on finding the sum of the first 9 terms of the geometric series 3 + 3^(4/3) + 3^(5/3) + ... The first term (a) is established as 3. The common ratio (r) is determined by dividing subsequent terms, specifically r = 3^(4/3) / 3 = 3^(1/3). Once the common ratio is identified, the standard formula for the sum of a geometric series can be applied to calculate the total sum of the series.

PREREQUISITES
  • Understanding of geometric series and their properties
  • Familiarity with the formula for the sum of a geometric series
  • Basic algebra skills for manipulating exponents
  • Knowledge of sequences and series concepts
NEXT STEPS
  • Learn how to derive the common ratio in geometric series
  • Study the formula for the sum of a geometric series: S_n = a(1 - r^n) / (1 - r)
  • Practice problems involving geometric series with varying terms
  • Explore applications of geometric series in real-world scenarios
USEFUL FOR

Students studying sequences and series, particularly those in high school mathematics, as well as educators looking for clear explanations of geometric series concepts.

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

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