please help me with part b of question 1 . i provided the program i wrote . I need to go though the program and prove it by induction with the steps claim, basis step, induction hypothesis and induction step . please do it with all these starps .

1. a. Write a recursive method octaldigitsum that takes a nonnegative integer parameter n and computes the sum of the digits of n when represented as an octal (base 8) number. For example, octalDigitSum (14) is 7 , since the decimal number 14 is 16 in octal. octaldigitsum (39) is 11. octaldigitSum (66) is 3. octaldigitsum (512) is 1. octaldigitsum (1) is 1. octaldigitSum (0) is 0 . Hint: Use the fact that the sum of the (octal) digits of n is the sum of the last (octal) digit (the ones digit) of n plus the sum of the (octal) digits of n/8. Turn in your code (hard copy only). b. Prove by induction on the length of the octal representation of n that the method returns the sum of the (octal) digits of n