Question

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

Answer 1

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!