Question

Which of the following series is NOT absolutely convergent?
A. the summation from n equals 1 to infinity of the quotient of negative 1 raised to the n plus 1 power and n
B. the summation from n equals 1 to infinity of the quotient of the quantity negative 1 and 2 raised to the nth power
C. the summation from n equals 1 to infinity of the quotient of negative 1 raised to the n plus 1 power and n raised to the 3 halves power
D. the summation from n equals 1 to infinity of the quotient of negative 1 raised to the n plus 1 power and the quantity n squared plus 1

Answer 1

|A| is just the Harmonic Series, so it diverges
|B| is just a GP with r = 1/2, so it converges
|C| sum 1/k^n converges for n>1
|D| a_n < 1/n^2 so it converges