I finding the sum of this series

In summary, the conversation is about finding the sum of a series and using the test for divergence to determine if the series converges. The solution involves breaking the series into two geometric series with different ratios.
  • #1
Randall
22
0

Homework Statement


Find the sum of the series from k=0 to infinity of ((4^k)-(3^k))/(5^k)

Homework Equations


I'm not sure exactly. I know the test for divergence is if lim n approaches infinity of the function from m=1 to infinity does not equal 0 then the series cannot diverge

The Attempt at a Solution


see attached but really my work is a lame attempt at a test for divergence, and not so much an attempt at the sum. Please I need help finding the sum.
 

Attachments

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  • #2
You're overlooking something very simple. It's difficult to give a hint without giving away the answer. Just think of the simplest thing you can do with the terms.
 
  • #3
Ahhhh. I see. This is simply the sum of two different geometric series - one with a ratio of 4/5 and one with a ratio of 3/5, yes? I feel silly now
 

FAQ: I finding the sum of this series

How do I find the sum of a series?

To find the sum of a series, you must first identify the pattern or formula for the series. Then, you can use mathematical techniques such as finding the common difference or common ratio, or using a formula for finite or infinite geometric or arithmetic series.

What is the difference between a finite and infinite series?

A finite series has a limited number of terms, while an infinite series has an infinite number of terms. This means that a finite series will eventually have an end, while an infinite series will continue on forever.

Can I use a calculator to find the sum of a series?

Yes, you can use a calculator to find the sum of a series. However, it is important to understand the underlying mathematical concepts and formulas so that you can verify the calculator's results and understand any errors that may occur.

What is the significance of finding the sum of a series?

Finding the sum of a series is important in various mathematical concepts such as calculus, probability, and statistics. It can also be used to solve real-world problems in fields such as finance, physics, and engineering.

Are there any shortcuts or tricks for finding the sum of a series?

Yes, there are various shortcuts and tricks for finding the sum of certain series, such as using the telescoping series method or the method of differences. However, it is important to understand the underlying concepts and not rely solely on shortcuts to ensure accurate results.

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