MATH 1132Q Lecture Notes - Lecture 10: Integral Test For Convergence, Improper Integral

• School: UConn
• Department: Mathematics
• Course: MATH 1132Q
• Professor: Dr. David McArdle

Document Summary

We are going to learn another test that can be performed on certain infinite series to determine if they converge (i. e. have a fixed, finite sum) or diverge (i. e. do not). This test is called the integral test and it involves comparing an infinite series to an improper integral. To be able to fully understand the integral test, we first need a way to visualize a series. To find if a series converges, we need to see if this area is a fixed, finite value! We will use what we know about improper integrals. To illustrate the idea if the integral test, we will consider t wo separate examples. Determine values of p for which the series converges and for which the series diverges. Using the integral test, we can determine that a given series converges but we cannot determine what it converges to. We can, however, get a good approximation by using partial sums.