Consider the following sum: S(n) = . (a) [5] Give a simple function f (n) so that the sum S(n) is in ( f (n)). (b) [5] State the definition of Big Oh. (c) [10] Use your definition of Big Oh from (b) to prove that S(n) is in O( f (n)) where f (n) is your answer to part (a). (d) [10] Prove that S(n) is in ( f (n)) where f (n) is your answer to part (a).