Integral Test: What should I compare this series with to prove it's convergence?

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SUMMARY

The discussion centers on applying the Integral Test to determine the convergence of a series. The series in question is compared to 1/n^1.5, which is known to be convergent. A specific comparison is suggested with the function √(2n + 2n)/n^2, reinforcing the similarity to 1/n^1.5. This establishes a clear path to proving convergence using the Integral Test.

PREREQUISITES
  • Understanding of the Integral Test for convergence
  • Familiarity with series comparison techniques
  • Knowledge of convergence criteria for p-series
  • Basic calculus concepts, including integration
NEXT STEPS
  • Study the Integral Test in detail, focusing on its application to series
  • Learn about p-series and their convergence properties
  • Explore examples of series comparisons using the Integral Test
  • Investigate advanced convergence tests, such as the Ratio Test and Root Test
USEFUL FOR

Students studying calculus, particularly those focusing on series and convergence tests, as well as educators looking for examples of the Integral Test in action.

theBEAST
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Homework Statement


Here is the problem:
http://dl.dropbox.com/u/64325990/HW%20Pictures/integraltest.PNG

The Attempt at a Solution


I know it is convergent because it is very similar to 1/n^1.5 which is convergent as well. However what would I compare this with using the Integral Test to prove that it is convergent?
 
Last edited by a moderator:
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theBEAST said:

Homework Statement


Here is the problem:
http://dl.dropbox.com/u/64325990/HW%20Pictures/integraltest.PNG

The Attempt at a Solution


I know it is convergent because it is very similar to 1/n^1.5 which is convergent as well. However what would I compare this with using the Integral Test to prove that it is convergent?

Compare it with \frac{\sqrt{2n+2n}}{n^2}. Then it's even more similar to 1/n^(1.5).
 
Last edited by a moderator:

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