I did figure out how to make Drracket do it 'the long way'. I used the recursive definitions we learned in class to make racket take the sum of the bottom layer of a pyramid then work its way up. It was pretty straight forward and looked like this
(require picturing-programs)
(define (sum n) (/ (* n (+ n 1)) 2))
(define (vol n)
(cond
[(equal? n 1) 1]
[else (+ (sum n) (vol (- n 1)))]))