How do you use the Alternating Series Test?
1 Answer
Oct 2, 2014
Alternating Series Test states that an alternating series of the form
converges if the following two conditions are satisfied:
#b_n ge b_{n+1}# for all#n ge N# , where#N# is some natural number.#lim_{n to infty}b_n=0#
Let us apply the test to the alternating series below.
In this series,
Let us check the two conditions.
#1/sqrt{n} ge 1/sqrt{n+1}# for all#n ge 1# #lim_{n to infty}1/n=1/infty=0#
Hence, we conclude that the alternating series converges.
I hope that this was helpful.