This applet illustrates the ε-M definition of convergence of a sequence.
Enter a rule for the sequence in the box provided. Drag the green point to adjust the value of L. Click 'Show ε' or 'Show M' to display points for ε and M, and their corresponding regions. For each ε, can you find an M so that all points in the blue region are also in the orange region? Zoom in or out using the buttons, if needed. You can add a second sequence for comparison by enabling 'Show second sequence'. Some interesting sequences to try:
  • - enter this as = (-1)^n
  • - enter this as = (-1)^n/n
  • - enter this as = (1+1/n)^n