Determine whether the series is convergent or divergent

Click For Summary
SUMMARY

The discussion centers on determining the convergence or divergence of a mathematical series. Participants emphasize the necessity of a complete problem statement, specifically the inclusion of a value for the variable x to assess convergence accurately. Additionally, they highlight that the presence of an equal sign within the summation notation is inappropriate. The consensus is that without a full and precise problem statement, the convergence cannot be evaluated correctly.

PREREQUISITES
  • Understanding of series convergence and divergence concepts
  • Familiarity with mathematical notation for summations
  • Knowledge of variable specifications in mathematical problems
  • Basic algebraic manipulation skills
NEXT STEPS
  • Research the criteria for series convergence, such as the Ratio Test and Root Test
  • Learn about proper summation notation and common pitfalls
  • Explore examples of series with specified variables to practice convergence analysis
  • Study the implications of incomplete problem statements in mathematical proofs
USEFUL FOR

Students in calculus or advanced mathematics, educators teaching series convergence, and anyone seeking to improve their problem-solving skills in mathematical analysis.

Fatima Hasan
Messages
315
Reaction score
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 ?
 

Attachments

  • png.png
    png.png
    540 bytes · Views: 425
  • 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
    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
    2 KB · Views: 511
  • gif&s=43.gif
    gif&s=43.gif
    2 KB · Views: 493
  • png.png
    png.png
    538 bytes · Views: 688
  • 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
    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
    2.1 KB · Views: 745
  • gif&s=18.gif
    gif&s=18.gif
    1.7 KB · Views: 672
  • gif&s=43.gif
    gif&s=43.gif
    2 KB · Views: 366
Last edited:
Physics news on Phys.org
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.
 
Orodruin said:
Is this the full problem statement?
Yes.
 
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.
 

Similar threads

Valid conclusion for an absolutely convergent sequence
  • · Replies 4 ·
Replies
4
Views
1K
Proving convergence and divergence of series
  • · Replies 3 ·
Replies
3
Views
2K
Determining if a series converges
  • · Replies 4 ·
Replies
4
Views
2K
Interval of convergence of power series from ratio test
  • · Replies 2 ·
Replies
2
Views
2K
Series investigation: divergence/convergence
  • · Replies 8 ·
Replies
8
Views
2K
Test the following series for convergence or divergence
  • · Replies 7 ·
Replies
7
Views
2K
Intervals of Convergence- Power Series
  • · Replies 11 ·
Replies
11
Views
3K
Absolute convergence of series
  • · Replies 2 ·
Replies
2
Views
1K
Is this series divergent or convergent?
  • · Replies 16 ·
Replies
16
Views
2K
Proving the convergence of series
  • · Replies 14 ·
Replies
14
Views
2K