Comparison test - sequences and series, Mathematics

Assignment Help:

Comparison Test

Assume that we have two types of series ∑an and ∑bn with an, bn ≥ 0 for all n and an ≤ bn for all n. 

Then,

A.  If ∑bn is convergent then this is ∑an.

B.  If ∑an is divergent then this is ∑bn.

Alternatively, we have two series of positive terms and the terms of one of the series are all time larger than the terms of the other series. After that if the larger series is convergent the smaller series must as well be convergent.  Similarly, if the smaller series is divergent as compared to the larger series must as well be divergent. 

Note: That in order to apply this test we require both series to start at similar place.


Related Discussions:- Comparison test - sequences and series

Algebra problem solving , A rectangles lenth is (x+4) and width is (x+3).By...

A rectangles lenth is (x+4) and width is (x+3).By adding binomials give its perimiter

What is slope of a line, What is Slope of a Line ? A line can have a "...

What is Slope of a Line ? A line can have a "steep" slope or a "gradual" slope. slope = rise/run The "rise" is the distance going up or down. The "run" is the distance goin

Precalulus, Solve the equation for exact solutions over the interval [o,2Pi...

Solve the equation for exact solutions over the interval [o,2Pi] 2 sec x + 1 = sec x + 3 Some one please help!!!

Math project , Topic 1: Statistical Studies Find two different news storie...

Topic 1: Statistical Studies Find two different news stories in a mainstream media source (CNN, FoxNews, Newsweek, etc.), that cite data from a recognized poling agency. Locate th

How to converting scientific notation to standard notation , How to Convert...

How to Converting Scientific Notation to Standard Notation ? To change a number in scientific notation to standard notation, move the decimal point the same number of places as

Division, How do i divide 200 by 4

How do i divide 200 by 4

Interval of convergence - sequences and series, Interval of Convergence ...

Interval of Convergence After that secondly, the interval of all x's, involving the endpoints if need be, for which the power series converges is termed as the interval of conv

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