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.

	1.
	2.
	3.
	4.
	5.

a.	p-series test
b.	comparison test with a geometric series
c.	ratio test
d.	integral test
e.	alternating series test

Answer 1

#1 is the only alternating series

#2 has terms easily shown to be smaller by comparison than the terms in the geometric 1/3ⁿ

#3 can be expressed as an improper integral

#4 can be shown to converge since the lim_n→∞ of the ratio a_n+1 / a_n = 0

#5 is a p-series with p = 1/7 (hence, divergent)