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

If t2+t+1=0 , t=w,w 2 L.H.S (w+w 2 ) + (w 2 + w) 2 ........  1  + 1 ....

t=w,w 2 L.H.S (w+w 2 ) + (w 2 + w) 2 ........  1  + 1 ..... But every third term is of the form: (w 3n +w 3n ) 2 =22 There are nine such terms. Their sum is 36. The rema

Shares and dividend, a man in rested rupee 800 is buying rupee 5 shares and...

a man in rested rupee 800 is buying rupee 5 shares and then are selling at premium of rupee 1.15. He sells all the shares.find profit

Probability transition matrices or brand switching, Define the Probability ...

Define the Probability Transition Matrices or Brand switching.

Solid mensuration., assuming that the earth''s sphere with a radius of 6400...

assuming that the earth''s sphere with a radius of 6400 km.. find the distance along a 3 degree arc at the equator of the earth''s surface?

Continuity, Continuity : In the last few sections we've been using the te...

Continuity : In the last few sections we've been using the term "nice enough" to describe those functions which we could evaluate limits by just evaluating the function at the po

#Regular Expression, Find the Regular Grammar for the following Regular Exp...

Find the Regular Grammar for the following Regular Expression: a(a+b)*(ab*+ba*)b.

Determine the total area of the land, John is planning to buy an irregularl...

John is planning to buy an irregularly shaped plot of land. Referring to the diagram, determine the total area of the land. a. 6,400 m 2 b. 5,200 m 2 c. 4,500 m 2 d.

Problem solving sequence: the operations, marianne took $100.00 to a store ...

marianne took $100.00 to a store that was holding a no-tax sale. she bought a shirt for $24.99, sandals for $18.50, shorts for $16.49, and a beach bag for $21.69. how much did she

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