11.2 Series, Convergence, and Divergence
Graphical view of the individual terms of the series vs. the Partial Sum
The applet below displays a graphical view of the individual terms of a series as well as the associated partial sum. If the graph for the partial sum appears to flatten out as then that suggests that the series converges and equals a finite value. In such a case, we must mathematically show that the series converges. If the graph for the partial sum does not appear to flatten out as then it suggests the series diverges. Caution: this applet does not provide sufficient proof or justification to argue that a series converges. Use the applet to support your intuition as well as to provide a visual representation of the series.