Determine whether the series is convergent or divergent

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Fatima Hasan
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Homework Statement


Infinite series sum from n = 0 to infinity of 1 divided by x to the n-th power, written in plain mathematical notation.


Homework Equations


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The Attempt at a Solution


Here's my work :
Typeset math: the sum from n=0 to infinity of 1/x^n, then the limit as n approaches infinity of 1/x^n equals 1/infinity equals 0, then 'Since lim a_n = 0, so it's divergent by n-th test.'

However , the correct answer is :

Typeset equation: sum from n = 0 to infinity of 1 over x^n equals x over (x minus 1), when |x| > 1.

Handwritten-style line of text reading: By the geometric series test, the series converges.


Can anyone tell me where's my mistake ?
 
Attachments
  • Infinite series sum from n = 0 to infinity of 1/(x^n).
    png.png
    540 bytes · Views: 458
  • Handwritten-style typeset derivation: sum from n=0 to infinity of 1/x^n equals 1/x^n; limit as n approaches infinity of 1/x^n equals 1/infinity equals 0; since lim a_n = 0, so it's divergent by nth test.
    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: 543
  • Handwritten-style line reading: By the geometric series test, the series converges.
    gif&s=43.gif
    2 KB · Views: 531
  • Infinite series sum from n = 0 to infinity of 1 divided by x to the n-th power, written in plain mathematical notation.
    png.png
    538 bytes · Views: 725
  • Typeset math: the sum from n=0 to infinity of 1/x^n, then the limit as n approaches infinity of 1/x^n equals 1/infinity equals 0, then 'Since lim a_n = 0, so it's divergent by n-th test.'
    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: 779
  • Typeset equation: sum from n = 0 to infinity of 1 over x^n equals x over (x minus 1), when |x| > 1.
    gif&s=18.gif
    1.7 KB · Views: 713
  • Handwritten-style line of text reading: By the geometric series test, the series converges.
    gif&s=43.gif
    2 KB · Views: 404
Last edited:

Discussion

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.
 

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