Question: Chapter 4, Trees: Show that if any complete, balanced tree has three children at every node its depth k = log 3 (2N + 1)

Chapter 4, Trees:

Show that if any complete, balanced tree has three children at every node its depth k = log 3 (2N + 1) where N is the total number of nodes in the tree including the root. (log 3 means log base three).

Hints: (1) show that 2N = 3k 1 (where k is the depth of the tree) then solve for k

(2) Start with N = SUM (3 i) for i = 0 to k. Find the sum of this finite geometric series.

Show all work, partial credit is given.

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