Series & Sequences — Professor's Edition

Select a Classic Example

Term $a_n$

Start $n$

Number of Terms ($N$)

Note: For convergence, the sequence of terms $a_n$ (red) must go to zero, but that does not guarantee the partial sums $S_n$ (blue) will stabilize.

A series $\sum a_n$ converges if the sequence of partial sums $S_n$ approaches a finite limit. In the graph above:

Red Points ($a_n$): These are the individual "steps" you are adding.
Blue Line ($S_n$): This is the total "height" reached after adding $n$ steps.

Series Convergence Visualizer