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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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The expert proves recurrence relationship of Catalan Numbers.

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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, ...

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