The Integral Test and Error Estimation Using p-Series

The area of the colored rectangles represents the sum of the series . With the rectangles in the starting (left) position, you can see that . Slide the rectangles to the right to see that . Thus the series and the integral converge or diverge together. For a convergent -series (or any convergent series satisfying the criteria of the integral test), the inequality holds for all , where is the partial sum. An option in this Demonstration lets you see this fact using . The gray rectangles represent , and the colored rectangles represent the "tail", .
  • Contributed by: Marc Brodie (Wheeling Jesuit University)

comments
 
Powered by Wolfram Mathematica
Give us your feedback
Give us your feedback

Source page:




 often  occasionally  never

Note: Please do not include anything you consider confidential or proprietary. Your message and contact information may be shared with the author of any specific Demonstration for which you give feedback, but will not otherwise be published or distributed.
Privacy Policy »

Note: To run this Demonstration you need the free
Mathematica Player
or Mathematica 7+
Download or upgrade to Mathematica Player 7
I already have Mathematica Player or Mathematica 7+