(Solved): Definition: A complete m-ary tree is a full m-ary tree in which every leaf is at the same level." ( ...

Definition: A complete $m$-ary tree is a full $m$-ary tree in which every leaf is at the same level." (i) Draw a complete binary tree of height 3. [1 mark] (ii) Write a formula for the number of node ${\mathrm{N}}_{\mathrm{d}}$ at a depth $\mathrm{d}$ of the tree. Note that the root node is at depth zero. [1 mark] (iii) Hence or otherwise, derive a formula, in terms of $\mathrm{n}$, for the total number of nodes $N_T$ in the tree of height $h$. [2 marks]