Question: A full k-ary tree is a (rooted) tree whose nodes either have exactly k children (internal nodes) or have no children (leaves). Using induction, formally

A full k-ary tree is a (rooted) tree whose nodes either have exactly k children (internal nodes) or have no children (leaves). Using induction, formally prove that every full k-ary tree that has x internal nodes has exactly kx + 1 nodes in total. Note that for full binary trees, i.e., when k = 2, this would imply that the total number of nodes is 2x + 1 (the total number of nodes of full binary trees is always odd).

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