# Series

# The Alternating Series Test Exercises

### Example 1

Find the first 5 partial sums of the alternating series

What do you notice about the partial sums?

### Example 2

Play with the alternating series

(a) Find the first 5 partial sums of this series. Write them so that each partial sum has a denominator of 32.

(b) Plot the sequence of partial sums on this graph:

(c) What do you notice about the behavior of the partial sums?

(d) Do you think this series converges? Why or why not?

### Example 3

For the series, can we use the AST to say the series converges? If not, why not?

### Example 4

For the series, can we use the AST to say the series converges? If not, why not?

### Example 5

For the series, can we use the AST to say the series converges? If not, why not?

### Example 6

For the series, can we use the AST to say the series converges? If not, why not?

### Example 7

For the series, can we use the AST to say the series converges? If not, why not?

### Example 8

Consider the alternating series

which converges by the AST. Find the error for each of the partial sums

(a) *S*_{9}

(b) *S*_{98}