Science:Infinite Series Module/Units/Unit 2/2.3 The Alternating Series Test/2.3.02 The Alternating Series Test

The alternating series test is given by the following.

The Alternating Series Test
If the alternating series $\sum _{k=1}^{\infty }(-1)^{k}a_{k}$ satisfies $a_{k}<a_{k-1}$ for k = 2, 3, 4, 5, ... , and $\lim _{k\rightarrow \infty }a_{k}=0$ then the series is convergent.

Take care to note that this test, as its name suggests, can only be applied for the special case when successive terms alternate between positive and negative values.