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(