Series Summation: Does the Ratio Test Determine Convergence or Divergence?

In summary, a series summation question is a mathematical problem that involves finding the sum of a sequence of numbers. There are various methods for solving these types of problems, including using formulas for different types of series. Some common types of series include arithmetic, geometric, harmonic, and alternating series. It is possible for a series to have an infinite sum, and these types of questions are important because they have real-world applications and help develop critical thinking and problem-solving skills.
  • #1
barksdalemc
55
0
I have this HW problem: Suppose Un and Vn are sequences of positve numbers such that the ratio of Un+1/Un will always we less than Vn+1/Vn. Show that 1) If Vn converges Un converged and 2) If Un diverges, Vn diverges.

I did the first part by showing that for any n, the ration of Un/Vn is decreasing and if lim of the ratio=M then Un=MVn.

Stuck on the second part.
 
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  • #2
ration=ratio
 

1. What is a series summation question?

A series summation question is a mathematical problem that involves finding the sum of a sequence of numbers, also known as a series. The series can be finite or infinite, and the goal is to find the total value of all the numbers in the sequence.

2. How do I solve a series summation question?

To solve a series summation question, you can use various methods such as the formula for arithmetic or geometric series, the sum of squares or cubes formula, or the telescoping series method. It is important to identify the type of series and choose the appropriate method to solve it.

3. What are some common types of series?

Some common types of series include arithmetic series, geometric series, harmonic series, and alternating series. Each type has its own unique properties and formulas for finding the sum of the series.

4. Can a series have an infinite sum?

Yes, a series can have an infinite sum. This means that the series continues on forever without ever reaching a finite value. An example of an infinite series is the harmonic series, which has a sum of infinity.

5. Why are series summation questions important?

Series summation questions are important because they have various real-world applications, such as in finance, physics, and computer science. They also help in developing critical thinking and problem-solving skills and are an essential concept in higher-level mathematics.

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