Write a recursive method octalDigitSum that takes a nonnegative integer parameter n and computes the sum...

 

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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). Prove by induction on the length of the octal representation of n that the method returns the sum of the (octal) digits of n. 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). Prove by induction on the length of the octal representation of n that the method returns the sum of the (octal) digits of n.

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