# 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.