11.1 Sequences and their Limits
Exploring the Terms of a Sequence
This applet explores the behavior of a sequence of terms as by visualizing the terms graphically. Enter the formula for the nth term of a sequence under "sequence rule". Adjust the slider for n to view more terms of the sequence.
Example 1: Consider the sequence given by , if we adjust the slider to n=100 we can see that the terms of the sequence appear to flatten out to a height of 2 at the far right of the graph. This suggests that equals 2. Now that you suspect the sequence converges to 2, you need to show it mathematically by evaluating the limit.
Example 2: Consider the sequence given by , if we adjust the slider to n=100 we can see that the terms of the sequence oscillate between -1 and 1 forever. This suggests that does not exist because successive terms of the sequence do not tend towards one particular value. Therefore, the sequence diverges.