Ratio test
Ratio test
In this lesson, we will learn about the ratio test. This test requires you to calculate the value of R using the formula below. If R is greater than 1, then the series is divergent. If R is less than 1, then the series is convergent. If R is equal to 1, then the test fails and you would have to use another test to show the convergence or divergence of the series. It is really recommended to use this test if your series has factorials in it. We will do a few questions which involve using the ratio test, and then look at a question that requires us to use the ratio test twice.
Lessons
Notes:
Note *Let $\sum a_n$ be a series. Then we say that
$R=$$\lim$_{n →$\infty$} $\mid \frac{a_{n+1}}{a_n}\mid$
Where:
1. If $R$ < $1$, then the series is convergent (or absolutely convergent)
2. If $R$ > $1$, then the series is divergent
3. If $R=1$, then the series could either be divergent, or convergent
Basically if $R=1$, then the ratio test fails and would require a different test to determine the convergence or divergence of the series.

2.
Convergence & Divergence of Ratio Test
Use the Ratio Test to determine if the series converges or diverges. If the ratio test does not determine the convergence or divergence of the series, then resort to another test.