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

Subspace of r containing n, Give an example of each of the following given ...

Give an example of each of the following given below . You do not require to give any justi cation. (a) A nonempty, bounded subset of Q with no in mum in Q. (b) A subspace of

Subset [tabular method], 1.A=the set of whole numbers less tan 4 ? 2.B=the ...

1.A=the set of whole numbers less tan 4 ? 2.B=the set of prime numbers less than 19 ? 3.C=the set of first three days of week?

Binimial, theory behind the greatest term in the binomial expansion

theory behind the greatest term in the binomial expansion

Determine the height of building, A 20-foot light post shows a shadow 25 fe...

A 20-foot light post shows a shadow 25 feet long. At the similar time, a building nearby casts a shadow 50 feet long. determine the height of building? a. 40 ft b. 62.5 ft

Prove gcd value, Let a, b, c 2 Z + . (a) Prove that if a|b, then ac|bc f...

Let a, b, c 2 Z + . (a) Prove that if a|b, then ac|bc for all c. (b) If a|bc, can you conclude that either a|b or a|c? Justify your answer with a proof or a counter example.

Write an equation in radius and solve it for radius, X and Y are centers of...

X and Y are centers of circles of radius 9cm and 2cm and XY = 17cm. Z is the centre of a circle of radius 4 cm, which touches the above circles externally.  Given that XZY=90 o , w

What is a lattice, What is a lattice? Which of the following graphs are lat...

What is a lattice? Which of the following graphs are lattice and why? Ans:  Let (L, ≤) be a poset. If each subset {x, y} consisting of any two elements of L, comprises a glb (I

Explain equation, Equation s(in Tth second)=u+at-a/2 seems to be dimensiona...

Equation s(in Tth second)=u+at-a/2 seems to be dimensionally incorrect.why?

Calculus, What is the slope of the line tangent to f(x)=3-2 ln(2x^2+4) at t...

What is the slope of the line tangent to f(x)=3-2 ln(2x^2+4) at the point (4, f(4))

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