$($ii$)(10\%)$ Consider a binary tree and answer the following questions.

$(10$a$)(4\%)$ Prove that if the height of the binary tree is $k,$ the maximum number of nodes is $2^k-1.$

$(10$b$)(6\%)$ Prove that if $n_0=$ number of leaf nodes, and $n_2=$ number of degree $-2$ nodes, the $n_0=n_2+1.$