In floating-point arithemetic on a computer, a divergent infinite series may have a finite sum.
This example was created to show that limited precision may affect terms in the infinite
series so that they eventually have no effect on the partial sum of the series.
As the terms become smaller and smaller, rounding error becomes more obvious.
To use the example below, select the preferred precision and press compute.
References: (Heath 15, Scientific Computing: An Introductory Survey)
- Does it take longer for the computer to calculate the partial sum if the precision is
increased? Why or why not?
- If you increase the precision to 5 digits how much closer is the partial sum
to the actual sum using exact arithmetic then using 3 digits of precision?
Applet Source sumseries.java,
Written by Nicholas Exner.