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    Catalan Numbers

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    Prove recurrence relationship of Catalan Numbers.

    Question: Let n be a non-negative integer. The number, x[n], of topologically distinct binary trees with n nodes can be shown to satisfy the following recurrence (x[0] = 1):

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    Please see the attached file for proof of Recurrence Relationship of Catalan Numbers by Mathematical Induction.

    This can be proved by the method of Mathematical Induction.

    Let P(n): , where and x[0] =1

    For n=1, ...

    Solution Summary

    The expert proves recurrence relationship of Catalan Numbers.