2. Chapter 10 sequences Series Tests find radius of convg R
geometric + telescoping
Mac series + important 7
Taylor
Binomial

3. SUMMARY OF TESTS Special Series: Series Tests Geometric Series
Harmonic Series
Telescoping Series
Alter Harmonic
p-series
Alternating p-series
Divergence Test
Integral Test
Comparison Test
Limit Compar Test
Ratio Test
Root Test
Alter Series Test

4. STRATEGY FOR TESTING SERIES
PART-1: Series with positive terms
STRATEGY FOR TESTING SERIES
Divg Test
factorial: ratio test  comp+lim comp
power of n: root test
easy to integrate: integral test
similar to geometric: try comp+lim comp
Similar to p-series: try comp+lim comp
PART-2: Alternating Series
Study (use PART-1)
convg
divg
use alt.-Test AC
convg
divg CC
PART-3: Series with some negative terms
REMARK:
For multiple-choice-question: before you start read the alternatives first. It guides you to which tests you need to use.
Study (use PART-1)
convg
divg AC

5. POWER SERIES 1 2 3 1 2 How to find R = radius of convergence Find:
(L is a function of x only)
Use ratio test: 3
How to find interval of convergence
Find R: 1
Study convg at endpoints: a+R and a-R 2

6. Important Maclaurin Series and Their Radii of Convergence
MEMORIZE: ** Students are required to know the series listed in Table 10.1, P. 620
Denominator is n!
even, odd
Denominator is n
odd

7. TAYLOR SERIES
Maclaurin series ( center is 0 )
Taylor series ( center is a )

8. THE RATIO AND ROOT TESTS
TERM-082

9. ABSOLUTE CONVERGENCE AND THE RATIO AND ROOT TESTS
TERM-082

10. ABSOLUTE CONVERGENCE AND THE RATIO AND ROOT TESTS
TERM-082

11. POWER SERIES
Final-101

12. POWER SERIES
Final-082

13. POWER SERIES
Final-102

14. POWER SERIES
Final-092

15. POWER SERIES
Final-092

16. POWER SERIES
Final-102