In this mathlet I provide an interactive and visually appealing tool for exploring convergence, divergence, and distribution of terms of sequences and series of constants. The user can enter an arbitrary sequence or series, choose a range (possibly minus to plus infinity), and the mathlet will plot one-by-one the consecutive terms or partial sums. The range can be changed without erasing already plotted terms, and optical zoom is provided for better viewing.
The mathlet contains several practice problems. In those problems, the user is encouraged to experiment and make guesses about convergence or distribution of terms before revealing the answer. The practice problems include examples where convergence or divergence is extremely slow, to illustrate the fact that making decisions about the limit by evaluating a few terms without knowing if the limit exists may not always work very well. Some of the practice problems show examples where terms of a sequence are dense in an interval and either uniformly distributed or not uniformly distributed. Those examples illuminate Weyl's Theorem on Uniform Distribution.
Open Sequences and Series Plotter in a new window
The mathlet will run on any machine with a generic browser as long as it has Flash Player 6 or higher. The free and small (668KB) Player can be easily downloaded and installed from the Macromedia site -- click on the button at the right. Netscape 6 or higher usually comes with the Player ready to use.