Determine whether the series is convergent or divergent

In summary, the conversation is about a homework problem involving a series that may or may not converge, but the problem statement is unclear and needs more information for a solution to be determined. The person asking for help has provided their attempted solution, but is unsure where they went wrong, and the other person is asking for the full problem statement to be reproduced accurately.
  • #1
Fatima Hasan
319
14

Homework Statement


png.png


Homework Equations


-

The Attempt at a Solution


Here's my work :
C%3Aso%20%5C%3B%5C%3Bit%27s%5C%3B%5C%3Bdivergent%5C%3B%5C%3Bby%5C%3B%5C%3Bn%5E%7Bth%7D%5C%3Btest.png

However , the correct answer is :

gif&s=18.gif

gif&s=43.gif


Can anyone tell me where's my mistake ?
 

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    C%3Aso%20%5C%3B%5C%3Bit%27s%5C%3B%5C%3Bdivergent%5C%3B%5C%3Bby%5C%3B%5C%3Bn%5E%7Bth%7D%5C%3Btest.png
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    C%3Aso%20%5C%3B%5C%3Bit%27s%5C%3B%5C%3Bdivergent%5C%3B%5C%3Bby%5C%3B%5C%3Bn%5E%7Bth%7D%5C%3Btest.png
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Last edited:
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  • #2
Is this the full problem statement? You need to specify a value for ##x## to know whether the series converges or not. Furthermore, there really should be no ##=## inside your sum.
 
  • #3
Orodruin said:
Is this the full problem statement?
Yes.
 
  • #4
Fatima Hasan said:
Yes.
I am sorry, but it cannot be the full problem statement. A full problem statement is not just a sum without specifications of what goes inside it. Please reproduce the full problem statement exactly as given.
 

1. What does it mean for a series to be convergent or divergent?

A convergent series is one in which the sum of its terms approaches a finite limit as more and more terms are added. In contrast, a divergent series is one in which the sum of its terms does not approach a finite limit and instead either approaches infinity or oscillates without approaching a limit.

2. How do you determine if a series is convergent or divergent?

There are several tests that can be used to determine if a series is convergent or divergent, including the comparison test, ratio test, and integral test. These tests involve evaluating the behavior of the series' terms and comparing them to known convergent or divergent series.

3. Can a series be both convergent and divergent?

No, a series cannot be both convergent and divergent. By definition, a series can only have one of these two properties. However, it is possible for a series to be conditionally convergent, meaning that it is convergent but only when certain conditions are met.

4. What is the difference between absolute and conditional convergence?

Absolute convergence refers to a series that is convergent regardless of the order in which its terms are added. In contrast, conditional convergence refers to a series that is only convergent when its terms are added in a specific order or under certain conditions.

5. Why is it important to determine if a series is convergent or divergent?

Determining if a series is convergent or divergent is important because it can provide valuable information about the behavior of the series and help in making predictions or calculations. Convergent series can also be used to approximate the value of certain functions, while divergent series may have no meaningful mathematical interpretation.

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