Question

If the summation of a sub n and the summation of b sub n are both series of positive terms and an < bn for all n, and the summation of b sub n diverges, then (15 points)

A) the summation of a sub n converges
B) the summation of a sub n diverges
C) the summation of a sub n = 0
D) the behavior of the summation of a sub n cannot be determined

Answer 1

D
Consider b_n = 1
a_n = 1/n^2
or
a_n = 1/n

∑1 surely diverges, but 1/n^2 converges, and 1/n diverges.