Prove that no matter what node we start at in a height-h binary search tree, k successive calls to "tree-successor" take O(k+h) time?

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Prove that no matter what node we start at in a height-h binary search tree, k successive calls to “tree-successor” take O(k+h) time?

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Check this SO post: algorithm - Prove the efficiency of repeated calls to successor() in binary trees? - Stack Overflow