Series proof: 1/1+(1/1+(1/1+(1/1+ what does it equal?

In summary, a series proof is a mathematical method used to determine the sum of an infinite series by adding up all the terms. To solve a series proof, one must identify the pattern and use mathematical techniques to simplify and find the sum. The formula for finding the sum of an infinite series is S = a / (1-r), but the value may vary depending on the method used. Series proofs have various real-world applications in fields such as finance, physics, and computer science.
  • #1
mxyplizk
8
0

Homework Statement


B=1/(1+(1/1+(1/1+(1/1+(1/1+...

what does B equal?


Homework Equations



I don't believe there are any...it's a conceptual question.


The Attempt at a Solution


Would it converge to 0? My reasoning was that if 1/(1+1)=1/2, and then 1/(1+1/2)=1/(3/2)=2/3, and 1/(1+(2/3))=1/(5/3)=3/5, and 1/(1+(5/3))=1/(8/3)=3/8, etc...
 
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  • #2
There's usually a way to algebraically manipulate this into a quadratic or similar problem. Have you tried that?

I can't quite remember how it goes, though...
 
  • #3
Oh, I remember.

Take a look at the denominator. The denominator CONTAINS B, as long as the series is infinite.
 
  • #4
Thanks for your help!
 
  • #5
No problem.
 

1. What is a series proof?

A series proof is a mathematical method used to determine the sum of an infinite series. This involves adding up all the terms in the series to come up with a final value.

2. How do you solve a series proof?

To solve a series proof, you must first identify the pattern or rule that the series follows. Then, you can use various mathematical techniques such as geometric or telescoping series to simplify the series and find the sum.

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

The formula for finding the sum of an infinite series is S = a / (1-r), where a is the first term in the series and r is the common ratio. This formula only works for convergent series, where the terms decrease in value as the series progresses.

4. Can a series proof have a different value depending on the method used?

Yes, a series proof can have a different value depending on the method used. This is because different methods may result in different simplifications of the series, leading to different final values. It is important to understand the limitations and assumptions of each method before using it to solve a series proof.

5. What are some real-world applications of series proofs?

Series proofs have many real-world applications, including in finance, physics, and computer science. For example, in finance, series proofs can be used to calculate compound interest and determine the future value of investments. In physics, series proofs can be used to solve problems related to motion and energy. In computer science, series proofs can be used to analyze algorithms and determine their time complexity.

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