linguistic:translation
Alternating series test

Suppose the following statements are true:

Then ∑ n = 1 ∞ (− 1) n a n {\displaystyle \sum _{n=1}^{\infty }(-1)^{n}a_{n}} and ∑ n = 1 ∞ (− 1) n + 1 a n {\displaystyle \sum _{n=1}^{\infty }(-1)^{n+1}a_{n}} are convergent series. This test is also known as the Leibniz criterion.