1. Ratio Test THE RATIO AND ROOT TESTS Series Tests Test for Divergence
Integral Test
Comparison Test
Limit Comparison Test
Ratio Test
be a series with positive terms

2. Ratio Test Example: Example: Example: THE RATIO AND ROOT TESTS
be a series with positive terms
Example:
Test the series for convergence.
Example:
Example:
Test the series for absolute convergence.
Test the series for absolute convergence.

3. Ratio Test REMARK: THE RATIO AND ROOT TESTS
be a series with positive terms
REMARK:
Case means that the test gives no information.

4. THE RATIO AND ROOT TESTS
TERM-101

5. Example: Root Test THE RATIO AND ROOT TESTS Series Tests
Test for Divergence
Integral Test
Comparison Test
Limit Comparison Test
Ratio Test
Test the series for convergence.
Root Test
be a series with positive terms

6. Example: Root Test THE RATIO AND ROOT TESTS
Test the series for convergence.
Root Test
be a series with positive terms

7. ABSOLUTE CONVERGENCE AND THE RATIO AND ROOT TESTS
TERM-091

8. ABSOLUTE CONVERGENCE AND THE RATIO AND ROOT TESTS
TERM-091

17. THE RATIO AND ROOT TESTS
TERM-082

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

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