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Recurrence Relations/Difference Equations

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Solve the following difference equations/recurrence relations:




Kindly show work in detail so I can understand the steps! Thanks!

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The expert solves recurrence relations and difference equations.

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I assume that n is a natural number and its count starts from 1, that is n = 1, 2, ...


(a) Lets rewrite it as x_{n+1} = n x_n and look at the first few values:

x_1 has some arbitrary value
x_2 = 1 * x_1
x_3 = 2 * x_2 = 2*1 * x_1
x_4 = 3 * x_3 = 3*2*1 * x_1
Here you can already guess that
x_n = (n-1)! * x_1
[You must have already learned about ...

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