Root test- sequences and series, Mathematics

Assignment Help:

Root Test- Sequences and Series

This is the final test for series convergence that we're going to be searching for at.  Like with the Ratio Test this test will as well tell whether a series is absolutely convergent or not rather as compared to simple convergence.

Assume that we have the series ∑an Define,

Then,

a. if L < 1  the series is absolutely convergent and therefore convergent).

b. if L > 1  the series is divergent.

c. if L =  1 the series may be divergent, may be conditionally convergent, or absolutely convergent.

Since with the ratio test, if we get L= 1 the root test will tell us nothing and we'll need to utilize another test to find out the convergence of the series.  As well note that if L=1 in the Ratio Test afterwards the Root Test will as well give L= 1.


Related Discussions:- Root test- sequences and series

Describe three ways to write negative fractions, Describe Three Ways to Wri...

Describe Three Ways to Write Negative Fractions? There are three different ways that a negative fraction can be written. They are all represent the same value. 1. The negative

Convert to scientific notation, 1 . If someone is 20 years old, deposits $3...

1 . If someone is 20 years old, deposits $3000 each year into a traditional IRA for 50 years at 6% interest compounded annually, and retires at age 70, how much money will be in th

Word problem, A girl has 25 plants in all, 8 of them are tomatos. She has 1...

A girl has 25 plants in all, 8 of them are tomatos. She has 10 more bean plants than pepper plants. How many pepper plants does she have?

What will the day of the week be the further time at the gym, Max goes to t...

Max goes to the gym every fourth day. Ellen's exercise routine is to go every third day. Today is Monday and both Max and Ellen are at the gym. What will the day of the week be the

Test, a piece of ribbon measures 2,25 meters . it is cut in half . how long...

a piece of ribbon measures 2,25 meters . it is cut in half . how long is one half of the ribbon

F distribution, The F Distribution The F distribution is the dis...

The F Distribution The F distribution is the distribution of the ratio of 2 random variables. Both random variables have yet another distribution, called the c 2 Distri

Differential equation - maple, 1. Consider the following differential equat...

1. Consider the following differential equation with initial conditions: t 2 x'' + 5 t x' + 3 x = 0, x(1) = 3, x'(1) = -13. Assume there is a solution of the form: x (t) = t

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd