# Series

# Convergence of Series Exercises

### Example 1

Find the *n*th partial sum of the series

for

(a) *n* = 1

(b) *n* = 3

(c) *n* = 5

### Example 2

Given the series

2 + 4 + 6 + 8 + 10 + ...

find

(a) *S*_{2}

(b) *S*_{4}

(c) *S*_{5}

### Example 3

For the series, find the first 4 terms of the sequence of partial sums.

3 + 8 + 13 + 18 + ...

### Example 4

For the series, find the first 4 terms of the sequence of partial sums.

### Example 5

For the series, find the first 4 terms of the sequence of partial sums.

### Example 6

Fill in the blank with either the word 'sequence' or the word 'series.'

For any BLANK there is a BLANK of partial sums.

### Example 7

Fill in the blank with either the word 'sequence' or the word 'series.'

A partial sum is a BLANK.

### Example 8

Fill in the blank with either the word 'sequence' or the word 'series.'

A BLANK is a sum of numbers.

### Example 9

Fill in the blank with either the word 'sequence' or the word 'series.'

A BLANK can be either finite or infinite.

### Example 10

Fill in the blank with either the word 'sequence' or the word 'series.'

A list of numbers separated by commas is called a BLANK.

### Example 11

Fill in the blank with either the word 'sequence' or the word 'series.'

We can always think of a BLANK as being infinite.