MHB Solving third order recurrence relation

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To solve a third order recurrence relation with a characteristic polynomial factored as (x-1)^3, the characteristic root r=1 has a multiplicity of 3. The general solution will take the form of a linear combination of terms involving powers of the root and polynomial factors, specifically: a_0 + a_1*n + a_2*n^2, where a_0, a_1, and a_2 are constants determined by initial conditions. The next step involves using the initial conditions to find these constants. This approach effectively addresses the recurrence relation.
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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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