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    Recursion

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    Determine whether each of these proposed definitions is a valid recursive definition of a function f from the set of non negative integers to the set of integers. If f is well
    defined, find a formula for f(n) when n is a non negative integer and prove that your formula is valid.
    a) f(0) = 1,f(n) = - f(n - 1) for n >= 1
    b) f(0) = 1, f(1) = 0, f(2) = 2, f(n) = 2f(n - 3) for n>=3
    c) f(0) = 0, f(1) = 1, f(n) = 2f(n + 1) for n >= 2
    d) f(0) = 0, f(1) = 1, f(n) = 2f(n - 1) for n >= 1
    e) f(0) = 2, f(n) = fen - 1) if n is odd and n >= 1 and f(n) = 2f(n - 2) if n >= 2

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    Solution Preview

    Determine whether each of these proposed definitions is a valid recursive definition of a function f from the set of non negative integers to the set of integers. If f is well
    defined, find a formula for f(n) when n is a non negative integer and prove that your formula is valid.
    a) f(0) = 1,f(n) = - f(n - 1) for n >= 1
    b) f(0) = 1, f(1) = 0, f(2) = 2, f(n) = 2f(n - 3) for n>=3
    c) f(0) = 0, f(1) = 1, f(n) = 2f(n + 1) for n >= 2
    d) f(0) = 0, ...

    Solution Summary

    Recursion is demonstrated for proposed functions.

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