Solving third order recurrence relation

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SUMMARY

The discussion focuses on solving a third order recurrence relation with a characteristic polynomial factored as (x-1)3. The characteristic root identified is r=1, which has a multiplicity of 3. The solution form for such a recurrence relation is established as a linear combination of terms involving the root raised to the power of n, specifically: an = A + Bn + Cn2, where A, B, and C are constants determined by initial conditions.

PREREQUISITES
  • Understanding of recurrence relations
  • Familiarity with characteristic polynomials
  • Knowledge of solving linear homogeneous equations
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the method of solving linear recurrence relations with constant coefficients
  • Learn about the implications of root multiplicity in recurrence relations
  • Explore initial condition applications in determining constants A, B, and C
  • Investigate related topics such as generating functions for recurrence relations
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Mathematicians, computer scientists, and students studying discrete mathematics or algorithm analysis who need to solve complex recurrence relations.

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I'm trying to solve a third order recurrence relation but not sure how. I wrote the characterisitc polynomial and factored it into [math](x-1)^3[/math]. Now what?
 
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Re: Solving third order reccurence relation

You have the characteristic root $r=1$ of multiplicity 3, so can you state what form the solution will have?
 

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