Education.com
Try
Brainzy
Try
Plus

# Sequences and Series for AP Calculus

(not rated)
By McGraw-Hill Professional
Updated on Oct 24, 2011

Practice problems for these concepts can be found at: Series Practice Problems for AP Calculus

### Series and Sequences

A sequence is a function whose domain is the non-negative integers. It can be expressed as a list of terms {an} = {a1, a2, a3, …, an, …} or by a formula that defines the nth term of the sequence for any value of n. A series is the sum of the terms of a sequence {an}. Associated with each series is a sequence of partial sums, {sn}, where s1 = a1, s2 = a1 + a2, s3 = a1 + a2 + a3, and in general, sn = a1 + a2 + a3 + … + an.

#### Example 1

Find the first three partial sums of the series .

Step 1:   Generate the first three terms of the sequence .

.

Step 2:   Find the partial sums.

#### Example 2

Find the fifth partial sum of the series .

Step 1:   Generate the first five terms of the sequence .

Step 2:   The fifth partial sum is .

### Convergence

The series converges if the sequence of associated partial sums, {sn}, converges. The limit where S is a real number, is the sum of series, and are convergent, then

#### Example 1

Determine whether the series converges or diverges. If it converges,find its sum.

Step 1: Find the first few partial sums.

Step 2: The sequence of partial sums {0.2, 0.24, 0.248, 0.2496, …} converges to 0.25, so the series converges, and its sum

#### Example 2

Find the sum of the series

Step 1:

Step 2:

Practice problems for these concepts can be found at: Series Practice Problems for AP Calculus

150 Characters allowed

### Related Questions

#### Q:

See More Questions

### Today on Education.com

Top Worksheet Slideshows