Question

How do you use a graphing calculator to find the limit of the sequence `a_n=(1/2)^n`?

Answer 1

`a_n` will approach ZERO.

Explanation:

Create the following table first.

And then we can use a graphical display calculator (I have used TI-84 Plus Silver Edition) for visually examining the graph.

n `a_n` Decimal form

1 1/2 0.5

2 1/4 0.25

3 1/8 0.125

4 1/16 0.625

and so on.

Enter the function using "Y=" Button on the calculator

For the "Window" Size, I have used the following:

`Y_min` = -0.5
`Y_max` = 0.5

All other entries remain as default entries.

Hit the "Graph" button to view the graph.

Use the "Trace" option to trace the points on the graph.

You can clearly see that for every incremented "n" value from 1, the corresponding `1/n` is moving toward ZERO.

Hence, we can conclude that the sequence `a_n = (1/2)^n` approaches ZERO.