Please help elaborately answer part (a). Thanks!

A binomial tree is a special kind of rooted tree used for various data structures in computer science. A degree d binomial tree can be defined recursively as follows. A degree 0 binomial tree is a single vertex with no edges. A degree d binomial tree has a root vertex with out-degree d. The first (that is, leftmost) subtree is a degree d - 1 binomial tree. The second (that is, second to left) subtree is a degree d - 2 binomial tree. Continue on in this way so that the last (rightmost) subtree is a degree 0 binomial tree. (a) What is the height of a degree d binomial tree? Prove your result by induction on d. (b) Write a recurrence for the number of nodes N(d) in a binomial tree of degree d. (c) Use the guess-and-check method to guess a formula for N(d). Prove that your formula holds by induction on d