Introduction to the Ratio Test
Let Σuk be a series with positive terms and suppose that
a) If ρ < 1, the series converges.
b) If ρ > 1 or ρ=+∞, the series diverges.
c) If ρ = 1, the series may converge or diverge, so that another test must be tried.
Problems Based On Ratio Test
Use the ratio test to determine whether the following series converge or diverge
1. Σ (1/k!)
Solution:
Since ρ < 1, the series converges.
3. Σ 1/[2k-1]
Solution: The ratio test is of no help since
Both the comparison test and the limit comparison test would also have worked here.
Root Test
In cases where it is difficult or inconvenient to find the limit required for the ratio test, the next test is sometimes useful.
Let Σuk be a series with positive terms and suppose that
a) If ρ < 1, the series converges.
b) If ρ > 1, the series diverges
c) If ρ = 1, the series may converge or diverge, so that another test must be tried.
Problems related to root test
Use the root test to determine whether the following series converge or diverge.
Since ρ > 1 we can say that the given series diverges.
Since ρ < 1, we can say that the series converges.
Now try it yourself! Should you still need any help, click here to schedule live online session with e Tutor!
About eAge Tutoring:
eAgeTutor.com is the premium online tutoring provider. Using materials developed by highly qualified educators and leading content developers, a team of top-notch software experts, and a group of passionate educators, eAgeTutor works to ensure the success and satisfaction of all of its students.
Contact us today to learn more about our tutoring programs and discuss how we can help make the dreams of the student in your life come true!