# An applet for teaching the limit of a sequence

I’m currently teaching real analysis. Right now we’re discussing limits of sequences. The definition is:

The limit of a sequence $(a_n)_{n=1}^\infty$ is $L$ (or converges to $L$) if, given any $\varepsilon>0$, there exists a natural number $N$ such that $|a_n-L|<\varepsilon$ for all $n\ge N$.

I used GeoGebra to create the following applet, which illustrates the definition of a limit. (Clicking on the previous link or the picture below will open the applet in a new window.)