Excercises for Series
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.
[, integral test.]
[ integral test].
[Divergent, divergent test].
[ telescoping sum].
[test for alternating series; note that this series converges 'conditionally', not absolutely.]
[test for alternating series; you need to prove is a decreasing function and its limit is
[converges conditionally; prove that is divergent by using limit comparison test with
Prove that converges conditionally.
[ use and use the ration test on
[convergent; use limit comparison test on