S. I only need question 6 done (discrete math). The other questions provide background information so you don't need to do them. Thanks! Suppose that T(0) = a and T(1) = b and are some constants. Define the running pairwiseaverage as, for n 2 0,1T(n + 2) = [T(n + 1) + T(n)]We are interested in the long-term behavior, i.e., what does T(n) look like as n → 0?1. Define the function of T as...F(x) = ) T(n) x"|n=0Use the recurrence relation on T to find an equation for F.2. Solve for F(x)3. Express F in terms of functions that you know the power series expansion for4. Give the power series expansion for F5. Give a general form for T(n) for n2 26. What is the limit of T(n) as n →→ o0?

We have to solve only question no 6

Answered: 6. What is the limit of T(n) as n → ∞?

Math

Advanced Math

6. What is the limit of T(n) as n → ∞?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

S. I only need question 6 done (discrete math). The other questions provide background information so you don't need to do them. Thanks!

Suppose that T(0) = a and T(1) = b and are some constants. Define the running pairwise
average as, for n 2 0,
1
T(n + 2) = [T(n + 1) + T(n)]
We are interested in the long-term behavior, i.e., what does T(n) look like as n → 0?
1. Define the function of T as...
F(x) = ) T(n) x"|
n=0
Use the recurrence relation on T to find an equation for F.
2. Solve for F(x)
3. Express F in terms of functions that you know the power series expansion for
4. Give the power series expansion for F
5. Give a general form for T(n) for n2 2
6. What is the limit of T(n) as n →
→ o0?

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