# Homework Help: Mathematical Induction (The inductive step)

1. Dec 13, 2011

### pavel329

1. I don't understand how to prove this.
for all n≥1, 10n - 1 is divisible by 9.

3. I've done the basis step.
Now i'm on the inductive step.
I'm using (10k+1-1)/9=1.
I don't know where to go from there.
Using algebra just gets me down to 10k+1= 10. And I really don't think that's the answer.
All examples i've seen show me things like 1...2..3..n+1= n(n+1) or something along the lines. They already give me the equation. This one does not.

Last edited by a moderator: Dec 13, 2011
2. Dec 13, 2011

### Staff: Mentor

This isn't right. You need to show that 10k+1-1 is divisible by 9, not that it is equal to 9. There is a difference. For example, 27 is divisible by 9, but the two numbers aren't equal.
What do you have for your induction hypothesis?

3. Dec 13, 2011

### ehild

Assume that 10k-1 is divisable by 9. Prove that it implies 10k+1-1 is also divisable by 9.

Try to bring 10k+1-1 to such form that it contain 10k-1.
10k+1=10*10k=> 10k+1-1=10*10k-1=10*10k-10+10-1=
10(10k-1)+9.
Can you proceed from here?

ehild