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

To find out the perimeter of a triangular give formula, To find out the per...

To find out the perimeter of a triangular region, what formula would you use? The perimeter of a triangle is length of surface a plus length of side b plus length of side c.

Analysis, Ask question #Minimum 1Let X be a topological space, let p ? X, a...

Ask question #Minimum 1Let X be a topological space, let p ? X, and let F and ? be C-valued functions on X that are continuous at p. Then the functions F + ?, F?, |F|, ReF and ImF

Trignometry, prove that cos(a)/1-sin(a)=tan(45+A/2)

prove that cos(a)/1-sin(a)=tan(45+A/2)

Daily Math, Six times as many people voted in the 2012 election as in the 2...

Six times as many people voted in the 2012 election as in the 2008 election.If 162 people voted in 2008,how many people voted in both elections?

Calculate zeros in the denominator of rational expressions, About Zeros in ...

About Zeros in the Denominator of Rational Expressions One thing that you must be careful about when working with rational expressions is that the denominator can never be zero

Fraction, Ask question #Minimum 100 words accepted

Ask question #Minimum 100 words accepted

Example of set theory, Suggest me the solution: Consider the given unive...

Suggest me the solution: Consider the given universal set T and its subjects C, D and E T = {0, 2, 4, 6, 8, 10, 12} C = {4, 8,} D = {10, 2, 0} E = {0} Find out

Exponents., the (cube square root of 2)^1/2)^3

the (cube square root of 2)^1/2)^3

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