If 0< a_n <b_n and the series a_n diverges then the series b_n diverges. Is this statement true or false?

1 Answer
May 9, 2018

True

Explanation:

This is the definition of the comparison test for series. This statement is most definitely true.

Let #a_n = 1^n# and #b_n = 2^n#. We can immediately see that

#0 < a_n < b_n#

And since #a_n = 1 + 1 + 1 + 1 + ...# which is clearly divergent

#b_n = 2 + 4 + 8 + 16 + ....# is also clearly divergent (it just approaches infinity quicker).

Hopefully this helps!