Purchase Solution

Real Analysis : Convergent Sequences and Limits

Not what you're looking for?

Ask Custom Question

Prove the sequence defined by a1 = 0, a2=1 and a(n+2)= (a(n+1)+a(n))/2 for n>=0, converges and find the limit.
(See attachment for full question)

Attachments
Purchase this Solution
Solution Summary

Convergent Sequences and Limits are investigated. The solution is detailed and well presented.

Solution Preview

Hello and thank you for posting your question to Brainmass!
The solution is attached below in two files. the files are identical in content, only differ in format. The first is in MS Word XP Format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.

For a proof that a monotonous bounded sequence converges see:
http://www-history.mcs.st-and.ac.uk/~john/analysis/Lectures/L8.html

For the geometric series sum see:
http://mathworld.wolfram.com/GeometricSeries.html

I use them both in the ...

Purchase this Solution
Free BrainMass Quizzes
Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Probability Quiz

Some questions on probability

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

View More Free Quizzes
Related BrainMass Solutions

  • Real Analysis : Convergent and Cauchy Sequences - Five Problems

    28850 Real Analysis : Convergent and Cauchy Sequences See attached file for all symbols. --- ? For each of the follwing statements decide if it is true or false.

  • Sequences and limits

    238692 Sequences and limits.

  • Sequences and limits

    Note: Here's Theorem 3.2.3 (a) Let X = (xn) and Y = (yn) be sequences of real numbers that converge to x and y respectively, and let c be an element R.

  • Sequences of Functions and Uniform Convergence

    98739 Real Analysis : Sequences of Functions and Uniform Convergence Discuss the convergence and the uniform convergence of each of the following sequences of functions on the given set D.

  • Real Analysis : Sequences

    Real analysis problems involving sequences are solved. The solution is detailed and well presented.

  • Converging and Diverging Sequences

    lim((-1)^n/(n+2)) lim((n^1/2)-1)/((n^1/2)+1)) lim((n+1)/(n(n^1/2))) establish the convergence and find the limits of the following sequences: ((1+1/n)^2n)) ((1+ (1/(n+1))) ((1-1/n)^n)) Problem #1 Because , then (a) is convergent.

  • Real analysis

    25761 Real analysis Prove: subsequences of a convergent sequences converge to the same limit as the original sequence See attached file This is a proof regarding subsequences of a convergent sequence.

  • Convergence and limits

    This provides an example of proving sequences are not convergent and working with limits.

  • Limits and sequences

    183641 Limits and sequences See attachment a. Use the definition of limits to show that b. Compute the following limits (justify your answers). 1. ( ) 2. c. Let ( be a sequence.

View More Related Solutions