Prove that (the number of 9s are the same); is the sum of the digits of the number .
Hello, James!
Prove that . . . the number of 9s is the same.
is the sum of the digits of the number .
. . Then: .
Since , then: .
. . That is: .
This is the number "moved" places to the left, plus a 1.
. . It contains 9's and an 8.
Therefore: . n-1)9 + 8 + 1\quad\Rightarrow\quad\boxed{ S(N^2) \;=\;9n}" alt="S(N^2) \:=\n-1)9 + 8 + 1\quad\Rightarrow\quad\boxed{ S(N^2) \;=\;9n}" />