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

Limit, limit x APProaches infinity (1+1/x)x=e

limit x APProaches infinity (1+1/x)x=e

Developing an understanding ones tens and more, DEVELOPING AN UNDERSTANDING...

DEVELOPING AN UNDERSTANDING :  The other day I was showing the children's book '203 Cats' to my 7-year-old niece. She had recently learnt how to write large numerals in her school

Gravity, There is a list of the forces which will act on the object. Gr...

There is a list of the forces which will act on the object. Gravity, F g The force because of gravity will always act on the object of course. Such force is F g   = mg

How to converting fractions to decimals explain with example, How to Conver...

How to Converting Fractions to Decimals explain with example? To convert fractions to decimals, divide the numerator by the denominator. The quotient is the decimal. Ex

Exponential functions, Exponential Functions : We'll begin by looking at t...

Exponential Functions : We'll begin by looking at the exponential function,                                                              f ( x ) = a x We desire to differe

What is 19% of 26, What is 19% of 26? To ?nd out 19% of 26, multiply 26...

What is 19% of 26? To ?nd out 19% of 26, multiply 26 through the decimal equivalent of 19% (0.19); 26 × 0.19 = 4.94.

Hcf and lcm, The HCF & LCM of two expressions are respectively (x+3) and (x...

The HCF & LCM of two expressions are respectively (x+3) and (x cube-7x+6). If one is x square+2x-3 , other is? Solution) (x+3) * (x^3-7x+6) = (x^2+2x-3) * y      ( ) (HCF*LCM=

Inside function and outside function, "Inside function" and "outside functi...

"Inside function" and "outside function : Generally we don't actually do all the composition stuff in using the Chain Rule. That can get little complexes and actually obscures the

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