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Solve the difference equation?

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1 Answer

yn+1

= [(n+1)/(n+2)]yn

= [(n+1)/(n+2)][n/(n+1)]yn-1

= [(n+1)/(n+2)][n/(n+1)]...[1/2]y0, up to n = 1

= [1/(n+2)]y0, after canceling out (n+1)!

or

yn = [1/(n+1)]y0, if you substitute n for n+1.