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

Critical points, Critical Point Definition : We say that x = c is a critic...

Critical Point Definition : We say that x = c is a critical point of function f(x) if f (c) exists & if either of the given are true. f ′ (c ) = 0        OR             f ′ (c

Explain pie charts, Explain Pie Charts ? If the frequencies are writte...

Explain Pie Charts ? If the frequencies are written as percentages, they can be easily compared using a pie chart. The following is an example of a pie chart using the data fr

Actual solution to a differential equation, The actual solution is the spec...

The actual solution is the specific solution to a differential equation which not only satisfies the differential equation, although also satisfies the specified initial conditions

Substitution, When I complete each of the three methods, should I get the s...

When I complete each of the three methods, should I get the same x and y values?

Mathematics is all around us-mathematics- in our lives, Mathematics Is All ...

Mathematics Is All Around Us :  What is the first thing you do when you get up? Make yourself a nice cup of tea or coffee? If so, then you're using mathematics! Do you agree? Cons

Find the distance of the bird from the girl, A boy standing on a horizontal...

A boy standing on a horizontal plane finds a bird flying at a distance of 100m from him at an elevation of 300. A girl standing on the roof of 20 meter high building finds the angl

Geometry, how you know that your first quadrilateral is an isosceles trapez...

how you know that your first quadrilateral is an isosceles trapezoid

Introduction to helping children learn mathematics, INTRODUCTION :  Do you...

INTRODUCTION :  Do you remember your school-going days, particularly your mathematics classes? What was it about those classes that made you like, or dislike, mathematics? In this

Linear algrebra, how do we solve multiple optimal solution

how do we solve multiple optimal solution

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