Department

MathematicsCourse Code

MAT136H1Professor

allStudy Guide

MidtermThis

**preview**shows half of the first page. to view the full**1 pages of the document.**11.4 Infinite Sequences & Series

Comparison Tests: Overview

The Comparison Test

If and are series with positive terms

1) If is convergent and for all , then is also convergent

2) If is divergent and for all , then is also divergent

Limit Comparison Test

For series with positive terms and , if

for a finite number , then both

series converge or both series diverge.

Estimating Sums

Based on the first number of terms in the series, the sum can be estimated. The error is than what

remains from the next term thereafter until infinity. This is calculated by

and its lower and upper limit can be set using improper integral:

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