Please help solve this question for me.

(a)Use mathematical induction to show that

S(n) = 3 × 2 n-1 -2

is the solution for the recurrence relation:

T(n) = 2T(n – 1) + 2 for n > 1 and T(1) = 1

(b) If 1 is added to the recurrence relation such that:

T(n) = 2T(n – 1) + 3 for n > 1 and T(1) = 0

What is the new equation for S(n)?