Suppose that T(0) = a ar average as, for n 2 0, %3D

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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Can you answer 3 and 4?

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?
Transcribed Image Text: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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