This interactive page is intended to demonstrate the definition of the limit of a sequence. There are four sequences to choose from.

• $$\{(0.9)^ne^{\frac{2\pi i}{n}}\}$$
• $$\{(-1)^n\times (0.01+(0.9)^ne^{\frac{n\pi i}{20}})\}$$
• $$\{(-1)^n\times ((0.9)^ne^{\frac{n\pi i}{20}})\}$$
• $$\{\frac{n^3-i}{n^3+i}\}$$
A yellow disc is displayed with a red dot at the centre that may (or may not) be the limit of the sequence.
• Zoom in or out, by pressing the appropriate buttons.
• Use the slider (or in older browsers) the drop down list to reduce the radius of the yellow disc by the chosen factor.
• Press Show sequence to see terms of the sequence plotted.
• Press Animate to see terms of the sequence plotted while $$\epsilon$$ decreases and we zoom in.
• Press 'Stop' to stop the plotting.