22a. Recursion Practice I 2019

1. (altsum) One way to see if a number is divisible by 11 is to find the alternating sum (+ then -) of the digits of the number, beginning at the ones digit, and see if that number is divisible by 11. The alternating sum of the digits if 1495 is 5-9+4-1 = -1, so 1495 is not divisible by 11. Design and test the function altsum: number(n) -> number.

   (check-expect (altsum 95) (+ 5 -9))
   (check-expect (altsum 1495) (+ 5 -9 4 -1))

2. (sum-octa) The n-th octagonal number is the number of dots that it takes to draw all of the edges of a regular octagon with n dots per edge. The formula for the n-th octagonal number is $3n^2-2n$, or (- (* 3 n n) (* 2 n)) in Racket.

   Write a function sum-octa: number(start) number(end) -> number to find the sum of all of n-th octagonal numbers beginning with n=start and ending with n=end.

   (check-expect (sum-octa 1 2) 9)
   (check-expect (sum-octa 2 5) 134)

   n	octagonal number n
   1	1
   2	8
   3	21
   4	40
   5	65