If a sequence is bounded and monotonic then it is convergent, Mathematics

Assignment Help:

Theorem

If {an} is bounded and monotonic then { an} is convergent. 

Be cautious to not misuse this theorem.  It does not state that if a sequence is not bounded and/or not monotonic that it is divergent.  The sequence in that instance was not monotonic but it does converge.

 Note: that we can make various variants of this theorem.  If {an}is bounded above and increasing after that it converges and similarly if {an} n a  is bounded below and decreasing after that it converges.

 


Related Discussions:- If a sequence is bounded and monotonic then it is convergent

Application of linear function, four times an unknown number is equal to tw...

four times an unknown number is equal to twice the sum of five and that unknown number

Multiplication properties, write a definition for associative property of m...

write a definition for associative property of multiplication in your own words and explain how you use it to compute 4*25*27 mentally

Center of mass - applications of integrals, Center of Mass - Applications o...

Center of Mass - Applications of integrals In this part we are going to find out the center of mass or centroid of a thin plate along with uniform density ρ. The center of mass

Greatest common factors, Lindy has 48 chocolate chip cookies and 64 vanilla...

Lindy has 48 chocolate chip cookies and 64 vanilla wafers. How many bags can lindy fill if she puts the chocolate chip cookies and the vanilla wafers in the same bags? She plans

Profit and loss, a man buy car at rs.50 and sells it at gain of 14% find ...

a man buy car at rs.50 and sells it at gain of 14% find the sp

Laws of indicies in fraction.., help to solve the laws of indicies chapter ...

help to solve the laws of indicies chapter 9c book 3 high school example19to the power3_2 what is answer

.., Ask quesLa proporción de empleados de una empresa que usan su auto para...

Ask quesLa proporción de empleados de una empresa que usan su auto para ir al trabajo es 5:16. Si hay un total de 800 empleados, diga la cantidad de autos que se espera que haya es

Process for solving linear equations, 1. If the equation has any fractions ...

1. If the equation has any fractions employ the least common denominator to apparent the fractions. We will do this through multiplying both sides of the equation by the LCD. Al

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