Scheme is the programming language should it be done

Recall that a function is tail recursive if its recursive call is the last operation in the function. A tail recursive function can be automatically converted by a compiler to use iteration, making it faster We have seen that a function can be made tail recursive by using a helper function, which we will call as accumulator, as in the following example. Original: (define (factorial n) (if (= n 0) 1 (* n (factorial (- n 1))) )) Tail recursive: (define (fact-accumulator n factpartial) (if (= n 0) factpartial (fact-accumulator (- n 1) (* n factpartial)) )) (define (factorial n) (fact-accumulator n 1)) We can write the tail recursive function also as follows. (define (factorial n) (letrec ((fact-accumulator (lambda (n factpartial) (if (= n 0) factpartial (fact-accumulator (- n 1) (* n factpartial)) ) ) (fact-accumulator n 1) )) Consider the following recursive function that computes the sum of squares of the first n numbers. (define sum-of-squares (lambda (n) (if (= n 0) 0 (+ (sum-of-squares (- n 1)) (* n n))))) a) Write a tail recursive version for the same function using letrec. b) Then, step through the evaluation of the original and tail recursive functions for (sum-of-squares 5). Write briefly about your observations