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    Recurrence Relations/Difference Equations

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    Solve the following difference equations/recurrence relations:

    a)

    b)

    c)

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

    © BrainMass Inc. brainmass.com December 15, 2022, 4:52 pm ad1c9bdddf
    https://brainmass.com/math/recurrence-relation/recurrence-relations-difference-equations-49806

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

    Solutions:

    (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 ...

    Solution Summary

    The expert solves recurrence relations and difference equations.

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