SUMMARY OF TESTS
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
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
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.
Final-121
Final-121
Final-122
Final-121
Final-131
Final-131
Final-131
Final-131
Final-122
Final-122
Final-122
Final-122
Final-122
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
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(