Convergence of Series Exercises

Example 1

Find the nth 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) S2

(b) S4

(c) S5

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.