Using mathematical induction, prove
is div. by
okie dokie, let's see where we get with this. i suppose you know the method of induction, so i won't explain it. let's just jump in
Let : " for all "
Clearly is true, since
So assume holds for some . That is, we can write for some . We show
Now is . We must show that this is divisible by 9, provided is.
Note that:
Since is an integer, we have that , as desired.
Thus, holds for all by induction.
QED