The alternating series test is given as:

, where , converges if is a monotone decreasing sequencewith limit zero.

I have 3 problems,I am asked to investigate these for conditional or absolute convergence, or divergence.

a)

b)

c)

for problem a) :

I think i should transform (a) into the form and then prove that is positive, and a monotone decreasing sequence with limit zero, to show that (a) converges. But how exactly can i show ? Don't know how to find the limit in this form ! Also,to test for absolute convergence of the series, do i merely test the series but exclude the factor ? i.e to test for absolute convergence do i test the convergence of:

a) ?

for b) :

Here r cannot be 1! do i just check from r=2? Getting (b) into the form to use the alternating series test i get

which leaves to be proven positive,and decreasing to limit zero. I thought about multiplying both numerator and denominator by n,to divide all terms by a dominant term ? to get

This seems to tend to zero as n tends to infinity. But now for absolute convergence, do i test to see if this converges ?