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Course: Calculus III
Topic: Sequences and Infinite Series
Subtopic: Integral Test & p-Series Test

Overview

The Integral Test can be used to determine if certain series, ones who meet very specific criteria, are convergent or divergent. Obviously integration is involved, so the explicit formula for the terms in the series must be integrable. This test has nice ties to the area under the curve and the "extra bits" that may be lost or gained when approximating a series. The process of writing a problem using the integral test if very specific both in notation and format. Attention to detail is necessary!

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 11.5.1 Use the integral test properly to determine if a series is convergent or divergent including understanding the conditions that must be met for its use
• 11.5.2 Consistently use proper notation and format when writing an integral test problem
• 11.5.3 Understand how the integral test for series relates to the area under the curve
• 11.5.4 Recognize a p-Series (Power Series) and know how to determine if it is convergent or divergent
• 11.5.5 Estimate the sum of a series that has positive term
• 11.5.6 Determine the "remainder", that is the error in approximating a series
• 11.5.7 Approximate the sum of a p-series
• 11.5.8 Apply the properties of convergent series as needed

Terminology

Define: theorem, hypothesis, conclusion, integral test, power series, p-series test, remainder (in terms of approximating or estimating the sum of a series)

Supplemental Resources (optional)

Paul's OL Notes - Calc II: Integral Test

Selwyn Hollis's Video Calculus: The Integral Test

Patrick JMT Just Math Tutorials: Integral Test for Series

More tutorial videos if you need them are listed at James Sousa's MathIsPower4U - Calc II. Scroll down middle column to "Infinite Series" for related titles.