Consider the following recurrence relation: Q(n) = { 42 = if n = 2∙Q(n-1)-3 ifn>
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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Consider the following recurrence relation:
<<<image here>>>
Prove by induction that Q(n) = 2n + 3, for all n ≥ 0
List the values of Q(n) for n less than or equal 10
![**Consider the following recurrence relation:**
\[
Q(n) =
\begin{cases}
4 & \text{if } n = 0 \\
2 \cdot Q(n-1) - 3 & \text{if } n > 0
\end{cases}
\]
**Tasks:**
1. Prove by induction that \(Q(n) = 2^n + 3\), for all \(n \geq 0\).
2. List the values of \(Q(n)\) for \(n\) less than or equal to 10.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc7f48373-fed3-413b-b0c3-3f0be25c6088%2Ff54fbeb0-67b3-49e4-b9b0-bbc6b1aa8804%2F8dl8toy_processed.png&w=3840&q=75)
Transcribed Image Text:**Consider the following recurrence relation:**
\[
Q(n) =
\begin{cases}
4 & \text{if } n = 0 \\
2 \cdot Q(n-1) - 3 & \text{if } n > 0
\end{cases}
\]
**Tasks:**
1. Prove by induction that \(Q(n) = 2^n + 3\), for all \(n \geq 0\).
2. List the values of \(Q(n)\) for \(n\) less than or equal to 10.
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