Let any number N=Sum(a_i*10^i) (i=0-n)
N=Sum((10^i-1)*a_i)+Sum (a_i)
Every item in Sum((10^i-1)*a_i) is divisible by 9. If Sum (a_i) is divisible by 9, then N must be divisible by 9.
N=Sum((10^i-1)*a_i)+Sum (a_i)
Every item in Sum((10^i-1)*a_i) is divisible by 9. If Sum (a_i) is divisible by 9, then N must be divisible by 9.