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ERJAEE, G. (20)

Lecture 23

Department

MathematicsCourse Code

MATH 2BProfessor

ERJAEE, G.Lecture

23This

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MATH 2B - Lecture 23 - Alternating Series

● The convergence tests that we have gone over so far apply only to series with

positive terms. Now we want to learn how to deal with alternating series whose

terms alternate in sign

Example:

● In general we show alternating series as:

● It is very important to understand that the part that causes the sign changes is

or and the term is representing the absolute value of the . So

is always positive

Theorem: Alternating series test

● If the alternating series

( for all n) or

for all n)

● Satisfy there two conditions:

1. (for all n decreasing)

2.

(only 0, not other number)

● Then the series is convergent

Example:

● We know that the harmonic series

is divergent. Now let’s consider the

alternating harmonic series

Solution:

●

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