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 [math]n\to\infty[/math] then that suggests that the series[math]\sum_{n=1}^{\infty}a_n[/math] 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 [math]n\to\infty[/math] then it suggests the series diverges.   [br][br]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.