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

What is the area of the square in simplified form, If the side of a square ...

If the side of a square can be expressed as a2b 3 , what is the area of the square in simplified form? Since the formula for the area of a square is A = s 2 , then by substitut

Help!!!, The equation -2x^2-kx-2=0 has two different real soultions. find t...

The equation -2x^2-kx-2=0 has two different real soultions. find the set of possible values for k.

The alternative hypothesis, The alternative hypothesis When formulatin...

The alternative hypothesis When formulating a null hypothesis we also consider the fact that the belief may be found to be untrue thus we will refuse it.  Therefore we formula

first and third quartiles, From the data given below calculate the value o...

From the data given below calculate the value of first and third quartiles, second and ninth deciles and forty-fifth and fifty-seventh percentiles.

Area under curve, Write a program to find the area under the curve y = f(x)...

Write a program to find the area under the curve y = f(x) between x = a and x = b, integrate y = f(x) between the limits of a and b. The area under a curve between two points can b

Math World Problem, The ratio of gasoline to oil needed to run a chain-saw ...

The ratio of gasoline to oil needed to run a chain-saw is 16:1. If you have 3.5 mL of oil, how many millilitres of gasoline must you add to get the proper mixture?

Example of cartesian coordinate graph, Example of Cartesian coordinate Grap...

Example of Cartesian coordinate Graph: Example:   The temperature of water flowing in a high pressure line was measured at regular intervals.  Plot the subsequent recorded da

Pricing, what is skimming pricing?

what is skimming pricing?

Transportation problem, 12. List the merits and limitations of using North ...

12. List the merits and limitations of using North West corner rule.

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