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Lecture 26

# MATH 2B Lecture Notes - Lecture 26: Ratio Test, Bmw 1 Series, Direct Comparison TestPremium

by OC1211656

Department

MathematicsCourse Code

MATH 2BProfessor

ERJAEE, G.Lecture

26This

**preview**shows half of the first page. to view the full**2 pages of the document.**03/06/2019

MATH 2B - Lecture 26 - Power Series

● A power series is a series of the form

○

■ Here x is the variable, is the coefficient

■ The main thing we are going to do is to find the values of x for

which the power series is convergent

Example:

● We take for all n, the power series becomes

● We know that

Geometric series

○

● Therefore, the power series

is convergent when |x|<1

More general, we can have

●

which is called a power

series centered at a

Example:

, for what values of x, does this power series converge

Solution:

● Again, this is a geometric series

○

○ → series is convergent

● For most of the power series, we use the ratio test or root test to find for which

values the series is convergent

Example:

For what values of x does the series

converge?

Solution:

● Ratio test

●

{ ,

● Therefore, the power series

is convergent when x = 0

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