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

Solution to a differential equation, A solution to a differential equation ...

A solution to a differential equation at an interval α Illustration 1:   Show that y(x) = x -3/2 is a solution to 4x 2 y′′ + 12xy′ + 3 y = 0 for x > 0. Solution : We'll

What is the evaluation of angle, In a periscope, a pair of mirrors is mount...

In a periscope, a pair of mirrors is mounted parallel to each other as given. The path of light becomes a transversal. If ∠2 evaluate 50°, what is the evaluation of ∠3? a. 50°

Evaluate infinity limit into the polynomial , Example   Evaluate following...

Example   Evaluate following limits. Solution Here our first thought is probably to just "plug" infinity into the polynomial & "evaluate" every term to finds out the

Saxon math, what is the are of a square that is 2 inches long and 2 inches...

what is the are of a square that is 2 inches long and 2 inches wide?

Calculate the value of expected value, The owner of TMH Hospital wants to o...

The owner of TMH Hospital wants to open a new facility in a certain area. He usually builds 25-, 50-, or 100-bed facilities, depending on whether anticipated demand is low, medium

Determines the possibility, There is a committee to be selected comprising ...

There is a committee to be selected comprising of 5 people from a group of 5 men and 6 women. Whether the selection is randomly done then determines the possibility of having the g

Geometric applications to the cross product, Geometric Applications to the ...

Geometric Applications to the Cross Product There are a so many geometric applications to the cross product also.  Assume we have three vectors a → , b → and c → and we make

Rate and ratio, express 4:24 as fraction in lowest term

express 4:24 as fraction in lowest term

2 step equations, What is a two step equation that equals 8 ?

What is a two step equation that equals 8 ?

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