Question

How do you do this question?

Answer 1

Answer:

None of the above

Step-by-step explanation:

According to the divergence test, if the limit of a sequence as n approaches infinity does not equal 0, then the series diverges.  (Notice that if the limit does equal 0, the series doesn't necessarily converge).

According to the geometric series test, a geometric series converges if -1 < r < 1, and diverges otherwise.

The first series is a geometric series with r = -5/3.  So it diverges.

The second series is also a geometric series:

3ⁿ⁻¹ / 2ⁿ = ⅓ (3ⁿ / 2ⁿ) = ⅓ (3/2)ⁿ

r = 3/2, so it diverges.

For the third series, the limit as n approaches infinity equals 1.  This fails the divergence test, so this series also diverges.

For the fourth series, the limit as n approaches infinity equals 1.  This fails the divergence test, so this series also diverges.