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    Fibonacci recurrence

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    Prove that the Fibonacci sequence can be obtained by the recurrence relationship.
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    Solution Preview

    Please see the attached file.

    This can be easily proved by Mathematical Induction:

    We show that the recurrence relationship holds for n = 2 and n=3 by direct substitution:
    At n =1 , G(1) =
    At n = 2, G(2) = = a + b = 1 (plugging ...

    Solution Summary

    The expert proves the Fibonacci sequence by the recurrence relationship. Mathematical induction is analyzed.