Question

In this task, you will write a proof to analyze the limit of a sequence. ASSUMPTIONS...

In this task, you will write a proof to analyze the limit of a sequence.

ASSUMPTIONS

Definition: A sequence {an} for n = 1 to ∞ converges to a real number A if and only if for each ε > 0 there is a positive integer N such that for all n ≥ N, |an – A| < ε .

Let P be 6. and Let Q be 24.

Define your sequence to be an = 4 + 1/(Pn + Q), where n is any positive integer

A. Compute a positive integer N that is appropriate to prove your sequence converges to a limit of 4. Show your work.

A.1. Using the formal definition provided in the Assumptions section, prove, for ε > 0, that an converges to a limit of 4. Justify your work.

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
In this task, you will write a proof to analyze the limit of a sequence. ASSUMPTIONS...
In this task, you will write a proof to analyze the limit of a sequence. ASSUMPTIONS Definition: A sequence {an} for n = 1 to ∞ converges to a real number A if and only if for each ε > 0 there is a positive integer N such that for all n ≥ N, |an – A| < ε . Let P be 6. and Let Q be 24. Define your sequence to be an = 4 + 1/(Pn +...
Assumptions: The formal definition of the limit of a function is as follows: Let ƒ :...
Assumptions: The formal definition of the limit of a function is as follows: Let ƒ : D →R with x0 being an accumulation point of D. Then ƒ has a limit L at x0 if for each ∈ > 0 there is a δ > 0 that if 0 < |x – x0| < δ and x ∈ D, then |ƒ(x) – L| < ∈. Let L = 4P + Q. when P = 6 and Q = 24 Define...
Using the definition of convergence of a sequence, prove that the sequence converges to the proposed...
Using the definition of convergence of a sequence, prove that the sequence converges to the proposed limit. lim (as n goes to infinity) 1/(n^2) = 0
Prove that a sequence (un such that n>=1) absolutely converges if the limit as n approaches...
Prove that a sequence (un such that n>=1) absolutely converges if the limit as n approaches infinity of n2un=L>0
) Let α be a fixed positive real number, α > 0. For a sequence {xn},...
) Let α be a fixed positive real number, α > 0. For a sequence {xn}, let x1 > √ α, and define x2, x3, x4, · · · by the following recurrence relation xn+1 = 1 2 xn + α xn (a) Prove that {xn} decreases monotonically (in other words, xn+1 − xn ≤ 0 for all n). (b) Prove that {xn} is bounded from below. (Hint: use proof by induction to show xn > √ α for all...
This problem outlines a proof that the number π is irrational. Suppose not, Then there are...
This problem outlines a proof that the number π is irrational. Suppose not, Then there are relatively prime positive integers a and b for which π = a/b. If p is any polynomial let Ip= ∫0a/bp(x) sinx dx. i. Show that if p is non-negative and not identically 0 on [0,a/b] then Ip>0; ii. Show that if p and all of its derivatives are integer-valued at 0 and a/b then Ip is an integer. iii. Let N be a large...
You’re the grader. To each “Proof”, assign one of the following grades: • A (correct), if...
You’re the grader. To each “Proof”, assign one of the following grades: • A (correct), if the claim and proof are correct, even if the proof is not the simplest, or the proof you would have given. • C (partially correct), if the claim is correct and the proof is largely a correct claim, but contains one or two incorrect statements or justications. • F (failure), if the claim is incorrect, the main idea of the proof is incorrect, or...
***Python Hailstones, also known as the Collatz sequence, are a mathematical curiosity. For any number in...
***Python Hailstones, also known as the Collatz sequence, are a mathematical curiosity. For any number in the sequence, the next number in the sequence is determined by two simple rules: If the current number n is odd, the next number in the sequence is equal to 3 * n + 1 If the current number n is even instead, the next number in the sequence is equal to one half of n (i.e., n divided by 2) We repeat this...
1. Write 3n + 1 Sequence String Generator function (1 point) In lab5.py complete the function...
1. Write 3n + 1 Sequence String Generator function (1 point) In lab5.py complete the function sequence that takes one parameter: n, which is the initial value of a sequence of integers. The 3n + 1 sequence starts with an integer, n in this case, wherein each successive integer of the sequence is calculated based on these rules: 1. If the current value of n is odd, then the next number in the sequence is three times the current number...
Activity 6.6. (a) A positive integer that is greater than 11 and not prime is called...
Activity 6.6. (a) A positive integer that is greater than 11 and not prime is called composite. Write a technical definition for the concept of composite number with a similar level of detail as in the “more complete” definition of prime number. Note. A number is called prime if its only divisors are 1 and itself. This definition has some hidden parts: a more complete definition would be as follows. A number is called prime if it is an integer,...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT