Question

Sum of the digits is also divisible by 9 "induction"

Answer 1

if n1 is a multiple of 9, take the sum of n1's digits. Let this sum = n2, then sum n2's digits and repeat until nk=9.

How would I use induction to prove that nk=9 for large enough k

my attempt:

base case: n1=r9, where r=1, then for k=1, nk=9

I have trouble finding the induction hypothesis for this question, I do know that 9|n1 and n1≡0(mod9)