Series: Steps on a Number Line
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Explore the sample series that illustrate convergence and divergence. Select various options to better see the steps. Adding up an infinite number of numbers does not always equal infinity. Notice that in each case the steps get smaller, a necessary condition for convergence. However, one of these example series diverges. (Which one?) Having smaller steps is not a sufficient condition for convergence.
Contributed by: Abby Brown and MathematiClub (Torrey Pines High School) (April 2007)
Open content licensed under CC BY-NC-SA