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SUMMARY OF TESTS
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Series Tests
1) Divergence Test
2) Integral Test
3) Comparison Test
4) Limit Compar Test
5) Ratio Test
6) Root Test
7) Alter Series Test
Special Series:
1) Geometric Series
2) Harmonic Series
3) Telescoping Series
4) Alter Harmonic
5) p-series
6) Alternating p-series
1
1
n
nar
1
1
nn
11)(
nnn bb
1
1
npn
0lim n
na
1)( dxxf
nn ab
n
n
n b
ac
lim
n
n
n a
aL 1lim
nn
naL
lim
0lim,,decalt
SUMMARY OF TESTS
1: rconvg
1
)1(
np
n
n
1
)1(
nn
n
divg
CC
1: pconvg
1:1:
pCCpAC
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4-types
1) Determine whether convg or divg AC,CC 2) Find the sum s
4) How many terms are needed
within error
Types of questions in the exam
5) Partial sums and their properties
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PART-1: Series with positive terms
1) Divg Test
2) factorial: ratio test comp+lim comp
3) power of n: root test
4) easy to integrate: integral test
5) similar to geometric: try comp+lim comp
6) Similar to p-series: try comp+lim comp
0lim n
na
nn 2
1
nn
n ua )1(
STRATEGY FOR TESTING SERIES
nn p1
1) Study (use PART-1)
PART-2: Alternating Series
na
convg
AC
divg
use alt.-Test
convg divgCC
na
1) Study (use PART-1) na
convg
AC
divg
PART-3: Series with some negative termsREMARK: For multiple-choice-question: before you start read the alternatives first. It guides you to which tests you need to use.
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4-types
1) Determine whether convg or divg AC,CC 2) Find the sum s
4) How many terms are needed
within error
Types of questions in the exam
5) Partial sums and their properties
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4) How many terms are needed within error
)()( errorrequirednn dxxfR
PART-1: Series with positive terms PART-2: Alternating Series
)( 1 errorrequirednn uR
na nnu)1(
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