David Little
Mathematics Department
Penn State University
Eberly College of Science
University Park, PA 16802
Office: 403 McAllister
Phone: (814) 865-3329
Fax: (814) 865-3735

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Sequences and Series

The following applet can be used to graph a sequence, an, and the corresponding series (i.e., the sequence of partial sums sn = a1 + a2 + ... + an). Simply enter an, the function that gives the nth term of the sequence. Keep in mind that the applet plots an for n≥ 1, so be sure that an is defined for all positive integers n.

The user can also choose between Comparison Test, Limit Comparison Test, Ratio Test and Root Test to help determine the convergence of the original series.

Note that for large values of x-scale, the applet does not plot every element of the sequence. To force the applet to plot every element of the sequence, hold down the "SHIFT" key. Keep in mind that doing so may slow down the applet.

Here is a list of functions that can be used with this applet.

Use the above applet to determine:

  • all the values of p ≥ 0 such that the sequence an = 1/np corresponds to a convergent series.
  • all the values of r such that the sequence an = rn corresponds to a convergent series.

© 2005 David P. Little
Download this applet for off-line viewing (includes source code). The above applet uses the Java Math Expression Parser (JEP) developed by Singular Systems