1. Use the Cauchy condensation test to establish the divergence of the series/;

a. sum(1/(n log(n))

b. sum(1/[n(log(n))(log log (n))])

2. Show that if a series is conditionally convergent, then the series obtained by its positive terms is divergent, and the series obtained by its negative terms is divergent.

3. give an example of a convergent series sum(a_n) such that sum(a_n^2) is not convergent.

4. If (a_n) is a decreasing sequence of strictly positive numbers and if sum(a_n) is convergent, show that lim(n a_n) =0

5. if (a_n) is a sequence and if lim(n^2 a_n) exists in the reals. show that sum(a_n) is absolutely convergent

show workThe Cauchy condensation test is demonstrated.

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