Please solve it

1. (10%) Let S = f(0) + f(2) + f(4) + ... + f(100). a) Express S using the (summation) notation. b) Evaluate the sum for S if f(k)= k/2 for all k. 2. (20%) Solve the following three recurrence relations and determine the order of growth for the solution of each of them. a) x(n)= x(n-1)+5 for n>0, x(0) = 0 b) x(n) = 3 x(n-1) for n > 0, x(0) = 5 c) x(n) = x(n/2) +n for n> 1, x(1)=1, assuming n is a power of 2, i.e., n=2, 4, 8, ..., 2k