Limit of a sequence

The limit of the sequence (an) is L if given any ε>0, there is an N>0 such that |an-L|<ε for all n≥N.

The yellow band is L±ε and the blue region correspons to those n≥N. The green dots are within ε of L and the red dots and red x's are not. The limit is L if for any given ε you must be able to move the blue region far enough to the right that there are no red x's.
This is a Java Applet created using GeoGebra from - it looks like you don't have Java installed, please go to
Use the sliders to change the values of ε and N.

Sequence: (your indexing variable must be n)
Proposed limit: L=

Note: right-click in the white region to zoom in or out or to change the scale of the axes. Shift-left-click and drag to move the axes.

Created by David Richeson using GeoGebra.