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10. Consider the following recurrence relation: P(n) = { 1 if n = 0 P(n-1)+n2 if n > 0. (a) Compute the first eight values of P(n). (b) Analyze the sequences of differences. What does this suggest about the closed-form solution? (c) Find a good candidate for a closed-form solution. (d) Prove that your candidate solution is the correct closed-form solution.

10. Consider the following recurrence relation: P(n) = { 1 if n = 0 P(n-1)+n2 if n > 0. (a) Compute the first eight values of P(n). (b) Analyze the sequences of differences. What does this suggest about the closed-form solution? (c) Find a good candidate for a closed-form solution. (d) Prove that your candidate solution is the correct closed-form solution.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 67E
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10. Consider the following recurrence relation: P(n) = { 1 if n = 0 P(n-1)+n2 if n > 0. (a) Compute the first eight values of P(n). (b) Analyze the sequences of differences. What does this suggest about the closed-form solution? (c) Find a good candidate for a closed-form solution. (d) Prove that your candidate solution is the correct closed-form solution.
Transcribed Image Text:10. Consider the following recurrence relation: P(n) = { 1 if n = 0 P(n-1)+n2 if n > 0. (a) Compute the first eight values of P(n). (b) Analyze the sequences of differences. What does this suggest about the closed-form solution? (c) Find a good candidate for a closed-form solution. (d) Prove that your candidate solution is the correct closed-form solution.
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