Proof of limit comparison test - sequences and series, Mathematics

Assignment Help:

Proof of Limit Comparison Test

As 0 < c <∞ we can find out two positive and finite numbers, m and M, like m < c < M .

 Now, as  

888_Proof of Limit Comparison Test - Sequences and Series.png

we know that for large enough n the quotient an/bn should be close to c and thus there must be a positive integer N like if n > N we as well have,

m < an / bn < M

Multiplying by bn provides

Mbn < an < Mbn

provided n > N .

Here now, if ∑bn diverges then thus does ∑mbn and so as mbn < an for all adequately large n by the Comparison Test ∑an as well diverges. 

Similarly, if  ∑bn converges then so does ∑Mbn and as an < Mbn for all sufficiently large n by the Comparison Test ∑an as converges.


Related Discussions:- Proof of limit comparison test - sequences and series

Class 10, The value of K for (k+1)x^2-2(k-1)x+1 = 0 has real and equal root...

The value of K for (k+1)x^2-2(k-1)x+1 = 0 has real and equal roots.

Integration, how to find area under a curve?

how to find area under a curve?

He would such as to leave 20% tip how much should he leave, Mr. Pelicas too...

Mr. Pelicas took his family out to dinner. The bill was $65.00. He would such as to leave a 20% tip. How much should he leave? Find 20% by multiplying $65 through the decimal e

Describe adding and subtracting square roots, Describe Adding and Subtracti...

Describe Adding and Subtracting Square Roots? To add or subtract square roots, the radicands must be the same. If the radicands are the same, add/subtract the coefficients (the

Basic operations on fractions, A simple example of fraction would be ...

A simple example of fraction would be a rational number of the form p/q, where q ≠ 0. In fractions also we come across different types of them. The two fractions

Solve out the linear equations, Solve out each of the following equations. ...

Solve out each of the following equations.                3( x + 5)= 2 ( -6 - x ) - 2x Solution In the given problems we will explained in detail the first problem and t

Can tan theeta be integrated?, Normal 0 false false false ...

Normal 0 false false false EN-IN X-NONE X-NONE MicrosoftInternetExplorer4

Creating input- output tables, How do I create an input-output table with t...

How do I create an input-output table with the rule -12

What is the probability of tossing a head, Q. What is the probability of to...

Q. What is the probability of tossing a head? List the sample space for tossing a coin once. What is the probability of tossing a head? Solution:  If you tossed a coin once

Geometry, Given: ??????? is supp. to ??????? ???? ????? bisects ??????? ?...

Given: ??????? is supp. to ??????? ???? ????? bisects ??????? ???? ????? bisects ??????? Prove: ??????? is a rt. ?

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