**Consider the following recurrence relation:**\[ P(n) = \begin{cases} 0, & \text{if } n = 0 \\ 5 \cdot P(n-1) + 1, & \text{if } n > 0 \end{cases} \]**Use induction to prove that** \[P(n) = \frac{5^n - 1}{4}, \text{ for all } n \geq 0.\]

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Answered: Consider the following recurrence…

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: SO, P(n) = {5· P(n – 1) + 1, if n = 0 if n > 0. 5n-1 Use induction to prove that P(n) = for all n>0. 4