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

Grade Average, Homework is worth 10% of my grade, quizzes are worth 30%, an...

Homework is worth 10% of my grade, quizzes are worth 30%, and tests are worth 40%. I have 15 grades in the homework section, they''re all 100''s. I have 2 grades in the quiz sectio

Shares and dividend, A man invests rs.10400 in 6%shares at rs.104 and rs.11...

A man invests rs.10400 in 6%shares at rs.104 and rs.11440 in 10.4% shares at rs.143.How much income would he get in all??

Estimate the probability - noncritical path , An advertising project manage...

An advertising project manager developed the network diagram shown below for a new advertising campagign.  In addition, the manager gathered the time information for each activity,

Decision theory, Decision Theory Decisions There are many types of ...

Decision Theory Decisions There are many types of decision making 1.      Decision making under uncertainty It refer to situations where more than one outcome can r

Determine the projection - vector, Determine the Projection of b = (2, 1, -...

Determine the Projection of b = (2, 1, -1) onto a = (1, 0, -2) There is a requirement of a dot product and the magnitude of a. a →  • b → = 4                             ||a

Positive real exponents, Simplify following and write the answers with only...

Simplify following and write the answers with only positive exponents.  (a) ( x 8.2 y -0.26 z 2 ) 0.5  (b)  (x 3 y -4.1   / x -2.7 ) -3 Solution  (a) (x 8.2

Logarithm, The function A(t) = 5(0.7)^t was used to define the amount A in ...

The function A(t) = 5(0.7)^t was used to define the amount A in milliliters of a drug in the bloodstream t hours after the drug was ingested. Determine algebraically the time it wi

Define histogram, Q. Define histogram? Ans. A histogram is a bar g...

Q. Define histogram? Ans. A histogram is a bar graph that gives the frequency of each value. Here are a few examples to illustrate the usefulness of this method of data r

Marketing plan and its parts, can you offer help with an entry level market...

can you offer help with an entry level marketing class and with developing charts and tables for the final marketing plan?

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