This demonstration allows you to input a series. It will then plot the terms in the associated sequence along with the terms in the sequence of partial sums. Hopefully seeing the visual of a sequence "leveling out" will help the student understand the idea of convergence.

You can type in any series. The slider for n allows you to plot up to the first 50 terms in the sequence. You can use the YMaximum slider to change the view if the terms in your sequence get big.
1. Try convergent series like 1 / n^2 or 1 / 2^n. Note how the points in red (terms of the sequence) converge to zero while the points in green (terms of the partial sums sequence) converge to some other value.
2. Try 1 / n and note that while the red points converge to zero, the green points continue to increase.
3. Try (n + 1) / n. Note that the red points converge but the green points continue to increase.