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Proof of the number of nodes in a binomial tree

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A binomial tree of height O, Bo is a one node tree. A binomial tree of height k, Bk is formed by attaching a binomial tree, Bk-1 to the root of another binomial tree another binomial tree Bk-1. Prove that a binomial tree Bk has 2to the power k nodes.

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Solution Summary

In this solution I provide an inductive proof that proves that the number of nodes in a binomial tree of height k is 2 to the power of k.

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We will use an inductive proof approach. This requires that we show
that for Bo the principle holds true and then, assuming Bk-1 holds
true then prove that Bk holds true. To make the statements easier
we'll say that the notation N(Bj) is the ...

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