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

Polynomials, for what value of k,the following system of equations have inf...

for what value of k,the following system of equations have infinite solutions?kx + 5y -(k-5)=0;20x +ky - k=0

Karls pearsons co-efficient of correlation, Aim: To test the significan...

Aim: To test the significant relationship between the accounting ratios of operating management and standard ideal ratios. Null Hypothesis(H 0 ) : There is no significa

Partial Differential Equations Walter A Strauss, Find the full fourier Seri...

Find the full fourier Series of e^x on (-l,l)in its real and complex forms. (hint:it is convenient to find the complex form first)

Solve the following word problems, 1.   The length of a rectangle is 2 time...

1.   The length of a rectangle is 2 times its width.  The area of the rectangle is 72          square inches. Find the dimensions of the rectangle.   2.   The length of a rec

Direction cosines - vector, Direction Cosines This application of the ...

Direction Cosines This application of the dot product needs that we be in three dimensional (3D) space not like all the other applications we have looked at to this point.

solve the game by linear programming, UA and DU are preparing for the NCAA...

UA and DU are preparing for the NCAA basketball game championship. They are setting up their strategies for the championship game. Assessing the strength of their "benches", each c

Complex eigenvalues, It is the last case that we need to take a look at. Th...

It is the last case that we need to take a look at. Throughout this section we will look at solutions to the system, x?' = A x? Here the eigenvalues of the matrix A are compl

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