Calculus 1000A/B Lecture Notes - Lecture 4: Infimum And Supremum, Binomial Series, Squeeze Theorem

• School: Western University
• Department: Calculus
• Course: Calculus 1000A/B
• Professor: Alan Mac Isaac

Document Summary

Given a sequence of real numbers a1, a2, a3, . , an, . a formal expression (5. 1) a1 + a2 + a3 + + an + = an. Xn=1 is called an in nite series, or just a series. We can add nitely many terms of the series to obtain. An = a1 + a2 + a3 + + an, , an, . are called the partial sums of the series (5. 1). They naturally form a sequence {an} of partial sums. If a = limn an and a is a nite number, then the seriesp an is called convergent, a is called its sum, and we write. If the sequence {an} is divergent (i. e. , a is in nite or does not exist), then the series (5. 1) is also called divergent. Perhaps the simplest example of an in nite series is the so-called geometric series a + aq + aq2 + + aqn + =