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CalcBC
Chp 113
Integral test and Estimate sum of a series
NOTES
1.
Sum of an infinite series
Previously used partial sums to create a general term of partial sums, S
n
,
such that the sum
of the infinite series is
.
This method is helpful only for some series.
Need
other methods to determine convergence and sums of series.
Other sections in this chapter
will be showing other methods for other series.
2.
GEOMETRIC SERIES
…
Look for common ratio.
The sum formula can be used if and only if the common ratio is
 r  < 1.
If the common ratio is
r
1
or
r
1,
then the series diverges.
3.
pSERIES
…
Look for the ratio as
If
p < 1,
then the series diverges
because it becomes
If
p = 1,
the series diverges
…
called a
HARMONIC SERIES
If
p > 1,
then the series CONVERGES
The denominator grows fast while the numerator stays as one value, the series very quickly
approaches insignificantly small amounts.
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View Full Document 4.
INTEGRAL TEST
…
Determines a series' converge
nce
Given
The gist is to
convert
a
n
to be
f(n)
and use
IMPROPER INTEGRALS
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This note was uploaded on 02/21/2011 for the course MATH 408C taught by Professor Knopf during the Spring '10 term at University of Texas at Austin.
 Spring '10
 KNOPF
 Infinite Series

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