Please show the guess is correct by induction... if guess isn't right propose and prove right one. #10P(n)={P(~S₁ ifif n=o2P(n-1)+n² ifm² noguess is:f(n) = 1+1 ² + 2 ² + 3² + ... + n²2=±n(n+1)(2n+1)6

To solve this problem, we need to use the principle of mathematical induction to prove that the…

Answered: #10 P(n)= {P(~ S₁ if if n=o 2P(n-1)+n²…

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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#10 P(n)= {P(~ S₁ if if n=o 2P(n-1)+n² if m² no guess is: f(n) = 1+1 ² + 2 ² + 3² + ... + n² 2 = ±n(n+1)(2n+1) 6