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

Example of factor by grouping, Factor by grouping each of the following. ...

Factor by grouping each of the following. 3x 2 - 2x + 12x - 8 Solution           3x 2 - 2x + 12x - 8 In this case we collect the first two terms & the final two te

Compute the probability, From past experience a machine is termed to be set...

From past experience a machine is termed to be set up correctly on 90 percent of occasions.  If the machine is set up correctly then 95 percent of good parts are expected however i

Point-slope form, The next special form of the line which we have to look a...

The next special form of the line which we have to look at is the point-slope form of the line. This form is extremely useful for writing the equation of any line.  If we know that

How are Indian customers visiting Shoppers’ Stop any differe, How are India...

How are Indian customers visiting Shoppers’ Stop any different from customers of developed western countries?

Round 468.235 to the nearest hundredth, Round 468.235 to the nearest hundre...

Round 468.235 to the nearest hundredth ? The hundredths place is the second digit to the right of the decimal point (3). To decide how to round, you must like as at the digit t

What is slope of a line, What is Slope of a Line ? A line can have a "...

What is Slope of a Line ? A line can have a "steep" slope or a "gradual" slope. slope = rise/run The "rise" is the distance going up or down. The "run" is the distance goin

Additionally functions in substitution rule, Substitution Rule Mostly ...

Substitution Rule Mostly integrals are fairly simple and most of the substitutions are quite simple. The problems arise in correctly getting the integral set up for the substi

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