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

Definition of vertical asymptote, Vertical asymptote Definition : The funct...

Vertical asymptote Definition : The function f(x) will contain a vertical asymptote at x = a if we contain any of the following limits at x = a .   x→a- Note as well that it

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

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

Pair of straight line, show that one of the straight lines given by ax2+2hx...

show that one of the straight lines given by ax2+2hxy+by2=o bisect an angle between the co ordinate axes, if (a+b)2=4h2

Example for comparison test for improper integrals, Example for Comparison ...

Example for Comparison Test for Improper Integrals Example:  Find out if the following integral is convergent or divergent. ∫ ∞ 2 (cos 2 x) / x 2 (dx) Solution

Calculate the fourier cosine series, The Fourier series expansion for the p...

The Fourier series expansion for the periodic function, f ( t ) = |sin  t | is defined in its fundamental interval. Taking π = 3.142, calculate the Fourier cosine series app

Example of intersection, Can anybody provide me the solution of the followi...

Can anybody provide me the solution of the following example? You are specified the universal set as T = {1, 2, 3, 4, 5, 6, 7, 8} And the given subjects of the universal s

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

Help, dividing decimals

dividing decimals

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