Excercises for Series

1. Remember (the statements for) the following: Recursive Sequences, -Series, geometric series, integral test, telescoping sum, comparison test, limit comparison test, ratio test, divergence test, test for alternating series.

2. [, integral test.]

3. [ integral test].

4. [integral test]

5. [Divergent, divergent test].

6. [ telescoping sum].

7. [test for alternating series; note that this series converges 'conditionally', not absolutely.]

8. [test for alternating series; you need to prove is a decreasing function and its limit is

9. [converges conditionally; prove that is divergent by using limit comparison test with

10. Prove that converges conditionally.

11. [ use and use the ration test on

12. [convergent; use limit comparison test on

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