Theorem

If {a_n} is bounded and monotonic then { a_n} 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 {a_n}is bounded above and increasing after that it converges and similarly if {a_n} n a  is bounded below and decreasing after that it converges.

 

Posted Date: 4/12/2013 3:17:02 AM | Location : United States

Ask an Expert

Related Discussions:- If a sequence is bounded and monotonic then it is convergent, Assignment Help, Ask Question on If a sequence is bounded and monotonic then it is convergent, Get Answer, Expert's Help, If a sequence is bounded and monotonic then it is convergent Discussions

Write discussion on If a sequence is bounded and monotonic then it is convergent
Your posts are moderated

Write your message here..

Related Questions

Detemine the amplitude of trigonometric function, 1. Consider the trigonome... 1. Consider the trigonometric function f(t) = (a) What is the amplitude of f(t)? (b) What is the period of f(t)? (c) What are the maximum and minimum values attained by

Math, how do you add all the Y.AND X UP WITH 3 how do you add all the Y.AND X UP WITH 3

Percentage, 7 is what percent of 105?. 7 is what percent of 105?.

Solve the form ax2 - bx - c factoring polynomials, Solve the form ax 2 - b... Solve the form ax 2 - bx - c factoring polynomials ? This tutorial will help you factor quadratics that look something like this: 2x 2 -3x - 14 (Leading coefficient is

Determine a particular solution to differential equation, Determine a parti... Determine a particular solution for the subsequent differential equation. y′′ - 4 y′ -12 y = 3e5t + sin(2t) + te4t Solution This example is the purpose that we've been u

Prove that sec2+cosec2 can never be less than 2, Prove that sec 2 θ+cosec 2... Prove that sec 2 θ+cosec 2 θ can never be less than 2. Ans:    S.T Sec 2 θ + Cosec 2 θ can never be less than 2. If possible let it be less than 2. 1 + Tan 2 θ + 1 + Cot

Dora, dora and her family are driving to visit relatives for the holidays t... dora and her family are driving to visit relatives for the holidays they travel 174 miles in 3 hours if they travel at a constant speed how many miles do they travel in one hourest

Determine the direction cosines and direction angles, Determine or find out... Determine or find out the direction cosines and direction angles for a = (2, 1, -4) Solution We will require the magnitude of the vector. ||a|| = √ (4+1+16) = √ (21)

In terms of x what is the area of her garden, Laura has a rectangular garde... Laura has a rectangular garden whose width is x 3 and whose length is x4. In terms of x, what is the area of her garden? Since the area of a rectangle is A = length times widt

Probability, An unbiased die is tossed twice .Find the probability of getti... An unbiased die is tossed twice .Find the probability of getting a 4,5,6 on the first toss and a 1,2,3,4 on the second toss