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

Subtraction of like terms with same signs, Suppose we are required to...

Suppose we are required to find the difference between 3abc and 7abc. We look at two scenarios. The value we would obtain by subtracting a larger quantity from th

Solids, a can of soup is shaped like wich solid

a can of soup is shaped like wich solid

Nine minus five times a number, Nine minus five times a number, x, is no le...

Nine minus five times a number, x, is no less than 39. Which of the subsequent expressions represents all the possible values of the number? Translate the sentence, "Nine minus

1, use 3/8 of a thin of paint, what fraction of the paint is left in thin (...

use 3/8 of a thin of paint, what fraction of the paint is left in thin (show work

Area, find area of rectangles and triangles put together

find area of rectangles and triangles put together

Fraction word problem, castor brought 6 3/4 carat cakes to share with 26 st...

castor brought 6 3/4 carat cakes to share with 26 students. did castor bring enough for each student to have 1/4 of cake?

Geometry, all basic knowledge related to geometry

all basic knowledge related to geometry

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