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

Rlc circuit, State clearly that the current in an RLC circuit with an AC so...

State clearly that the current in an RLC circuit with an AC source with and without the use of complex variables

Coordinate geometry, find the points on y axis whose distances from the poi...

find the points on y axis whose distances from the points A(6,7) and B(4,-3) are in the ratio 1:2

If pth term of ap is q and qth term is p. p.t its nth term, If the p th te...

If the p th term of an AP is q and the q th term is p. P.T its n th term is (p+q-n). Ans:    APQ a p = q a q = p a n = ? a + (p-1) d = q a + (q-1) d = p

Find the third vertex of a triangle, Find the third vertex of a triangle if...

Find the third vertex of a triangle if its two vertices are (-1, 4) and (5, 2) and mid point of one side is (0, 3).

Trigonometry, Show that the radius of the circle,passing through the centre...

Show that the radius of the circle,passing through the centre of the inscribed circle of a triangle and any two of the centres of the escribed circles,is equal to the diameter of t

Problem solving, Sales price of a compact disc player is $200, each new cd ...

Sales price of a compact disc player is $200, each new cd is on sale for $12. kyle purchases a player and some cds for $224. how many cds were purchased?

Circles, assignment on theorems on circle for class 9

assignment on theorems on circle for class 9

Explain binomial distribution, Q. Explain Binomial Distribution? Ans. ...

Q. Explain Binomial Distribution? Ans. The binomial distribution occurs when you are considering the probability function of a binomial experiment. Binomial Experiment

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