Question

Question 4 Let a sequence {an}∞ n=1 a sequence satisfying the condition ∀c ∈ (0, 1),...

Question 4 Let a sequence {an}∞ n=1 a sequence satisfying the condition ∀c ∈ (0, 1), ∀n ∈ N, | a_(n+2) − a_(n+1) | < c |a_(n+1) − a_n |.

4.1 Show that

∀c ∈ (0, 1), ∀n ∈ N, n ≥ 2, | a_(n+1) − a_n | < c^(n−1) | a_2 − a_1 |.

4.2 Show that {an}∞ n=1 is a Cauchy sequence

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Problem 1. Let {En}n∞=1 be a sequence of nonempty (Lebesgue) measurable subsets of [0, 1] satisfying...
Problem 1. Let {En}n∞=1 be a sequence of nonempty (Lebesgue) measurable subsets of [0, 1] satisfying limn→∞m(En) = 1. Show that for each ε ∈ [0, 1) there exists a subsequence {Enk }k∞=1 of {En}n∞=1 such that m(∩k∞=1Enk) ≥ ε
Additional Problem: Suppose we know that 1+i is a solution to the equation a_0+ a_1 z...
Additional Problem: Suppose we know that 1+i is a solution to the equation a_0+ a_1 z + a_2 z^2 + ... +a_n z^n=0, where the coefficients a_0, a_1, a_2, etc are all real numbers. Can you find another solution to the equation? If yes, what is it? Explain why.
Let {s_n} be a sequence of positive numbers. Show that the condition lim as n-> infinity...
Let {s_n} be a sequence of positive numbers. Show that the condition lim as n-> infinity of (s_n+1)/(s_n) < 1 implies s_n -> 0
Let 0 < θ < 1 and let (xn) be a sequence where |xn+1 − xn|...
Let 0 < θ < 1 and let (xn) be a sequence where |xn+1 − xn| ≤ θn  for n = 1, 2, . . .. a) Show that for any 1 ≤ n < m one has |xm − xn| ≤ (θn/ 1-θ )*(1 − θ m−n ). Conclude that (xn) is Cauchy b)If lim xn = x* , prove the following error in approximation (the "error in approximation" is the same as error estimation in Taylor Theorem) in t:...
a) Let y be the solution of the equation y ′ − [(3x^2*y)/(1+x^3)]=1+x^3 satisfying the condition  y...
a) Let y be the solution of the equation y ′ − [(3x^2*y)/(1+x^3)]=1+x^3 satisfying the condition  y ( 0 ) = 1. Find y ( 1 ). b) Let y be the solution of the equation y ′ = 4 − 2 x y satisfying the condition y ( 0 ) = 0. Use Euler's method with the horizontal step size  h = 1/2 to find an approximation to the value of the function y at x = 1. c) Let y...
Let (a_n)∞n=1 be a sequence defined recursively by a1 = 1, a_n+1 = sqrt(3a_n) for n...
Let (a_n)∞n=1 be a sequence defined recursively by a1 = 1, a_n+1 = sqrt(3a_n) for n ≥ 1. we know that the sequence converges. Find its limit. Hint: You may make use of the property that lim n→∞ b_n = lim n→∞ b_n if a sequence (b_n)∞n=1 converges to a positive real number.  
4.2 Given a sequence x(n) for 0 ≤ n ≤ 3, where x(0) = 4, x(1)...
4.2 Given a sequence x(n) for 0 ≤ n ≤ 3, where x(0) = 4, x(1) = 3, x(2) = 2, and x(3) = 1, evaluate its DFT X(k). 4.5 Given the DFT sequence X(k) for 0 ≤ k ≤ 3 obtained in Problem 4.2, evaluate its inverse DFT x(n).
4. Let an be the sequence defined by a0 = 0 and an = 2an−1 +...
4. Let an be the sequence defined by a0 = 0 and an = 2an−1 + 2 for n > 1. (a) Find the value of sum 4 i=0 ai . (b) Use induction to prove that an = 2n+1 − 2 for all n ∈ N.
Exercise 1. Suppose (a_n) is a sequence and f : N --> N is a bijection....
Exercise 1. Suppose (a_n) is a sequence and f : N --> N is a bijection. Let (b_n) be the sequence where b_n = a_f(n) for all n contained in N. Prove that if a_n converges to L, then b_n also converges to L.
Determine whether the sequence a_n = (3^n + 4^n)^(1/n) diverges or converges
Determine whether the sequence a_n = (3^n + 4^n)^(1/n) diverges or converges
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT