Problem L Power series are typically used to "break" a function into a sequence of numbers (the Taylor coeffi- cients of the function). However, sometimes it is useful to go in the opposite direction, assembling a sequence of numbers into a function. Let fn be the n-th Fibonacci number of Example 3c in 8.1, k=n k=n An = > k = 1+2+ ... +n , Bn = >k2 = 12 + 22 + ... + n2; by definition fo = Ao = Bo = 0. (a) Give a recursive definition of the numbers fn, An, Bn with n 2 0. (b) Use mathematical induction and only part (a) to show that fn, An, Bn Andn, B(x) = Bran , n=0 n=0 converge if x|