Physics 374
Fall 2004
Pro. E. F. Redish

The object of this problem is to use your new knowledge of tables in Mathematica to investigate how quickly different infinite series converge.  A simple result from calculus is that (∑_(n = 0)^∞) (x^n) = (1/(1 - x)) for all |x| < 1, so for example, (∑_(n = 0)^∞)((((1/3)))^n) = (3/2).  Plot a graph of (∑_(n = 0)^y)((((1/3)))^n)  vs. y, making sure to include y's up to a large enough value to clearly show convergence of the sum.  Since y is discreet in nature, the choice of tables and ListPlot is a natural one.  Note the PlotRange command, like we talked about in the first Mathematica lesson, works with ListPlot as well, which should help with formatting your graphs.  Compare this with how (∑_(n = 0)^y)((((2/3)))^n)  converges to 3 and how (∑_(n = 0)^y)((((9/10)))^n)  converges to 10.  Do your graphs match what you'd expect?  Explain.

(Problem by T .  Bing)