Integral Test: Analyzing 1/(n+1)^x with x > 1

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SUMMARY

The discussion centers on applying the integral test to evaluate the series sum from n=0 to infinity of 1/(n+1)^x, where x > 1. The user initially struggled with the variable x in the integral but found clarity by substituting x with a constant, a. This substitution facilitated the evaluation of the integral, leading to a successful application of the integral test. The integral test confirms the convergence of the series for values of x greater than 1.

PREREQUISITES
  • Understanding of the integral test for convergence
  • Familiarity with series and sequences in calculus
  • Basic knowledge of integration techniques
  • Ability to manipulate algebraic expressions
NEXT STEPS
  • Study the integral test for convergence in more detail
  • Learn about convergence criteria for p-series
  • Explore substitution methods in integration
  • Investigate the implications of series convergence in real analysis
USEFUL FOR

Students and educators in calculus, mathematicians focusing on series convergence, and anyone interested in advanced integration techniques.

brunette15
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Hi,
I am trying to use an integral test on the following series:

The sum from n=0 to infinity on 1/(n+1)^x where x>1

I know the process of using the integral test however i am unsure as to how to evaluate the integral with the x in the series :/

Thanks in advance!
 
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Maybe using $x$ confuses you. Try putting $x=a$, what do you have? Can you write down your attempt?
 
ZaidAlyafey said:
Maybe using $x$ confuses you. Try putting $x=a$, what do you have? Can you write down your attempt?

Yes i think using x was a little confusing. I was able to get it thankyou!
 

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