Match each series to the test that should be used to test for convergence/divergence. While it is possible that each test could apply to more than one series, in this exercise each is only used once.

Question

Match each series to the test that should be used to test for convergence/divergence. While it is possible that each test could apply to more than one series, in this exercise each is only used once.

a.	alternating series test
b.	geometric series test
c.	ratio test
d.	nth term test

Answer 1

in order: alternating series, nth term, ratio, geometric series

The 4th series is the only one that is geometric. With that taken, the first is the only alternating (signs) series. We can apply the n^th term test to the n² series, because the lim_n→∞ n² ≠ 0, so the series diverges. The ratio of the n+1^st term to the nth term in 2ⁿ/n! , 2/(n+1), is sufficient to show convergence.