MATH 1132Q Lecture Notes - Lecture 9: Convergent Series
65
MATH 1132Q Full Course Notes
Verified Note
65 documents
Document Summary
Given a sequence we can make an infinite series by adding all of the terms of the sequence! No, we will not always get a sum of infinity. Our job is to determine when a given series will converge (i. e. the sum is a fixed finite value) and when it will diverge (i. e. the sum is not a fixed finite value). One way to determine if a series has a sum (i. e. a fixed, finite sum) is to consider partial sums. In this way we create a sequence of partial sums . The limit of this sequence (i. e. when n goes to infinity) will represent the sum of the original series! If the sequence is convergent and then the series is called convergent and we write: The number s is called the sum of the series. If the sequence is divergent, then the series is divergent. exists as a real number,
