Sequences and series
This applet shows the relationship between terms of a sequence and the partial sums of a series. It also allows exploration of some important sequences & series including geometric and harmonic sequences.
Choose a sequence from the drop-down menu (or choose ‘Enter your own’ and type one in). Drag the slider at the bottom of the screen to show more or less terms of the sequence.
Does the sequence converge? If so, what is its limit? Click ‘Show limit of sequence’ to check.
Click ‘Show series’ to show the partial sums $p_n$. What happens to them as $n \to \infty$? Click ‘Show sum of series’ to check.