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Show that the tree height of a height-balanced binary search tree with n nodes is O(log...

Show that the tree height of a height-balanced binary search tree with n nodes is O(log n). (Hint: Let T(h) denote the fewest number of nodes that a height-balanced binary search tree of height h can have. Express T(h) in terms of T(h-1) and T(h-2). Then, find a lower bound of T(h) in terms of T(h-2). Finally, express the lower bound of T(h) in terms of h.)

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T(h) >2 x T(h-2)> 2 x T (h-4)> 2 x 2 x 2 x T(h-6) >21 x T(h-2xj) Where, j is any positive integer Substitute (h-2 xj) 2 in th

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