# Mathematical Induction help!!

• May 6th 2013, 01:18 PM
zhengcl86
Mathematical Induction help!!
prove that for all n>1 , 10^n -1 is divisible by 9. Include both a basis step and an inductive step.

so for the basis step i have

let n =1 10(1) - 1 / 9
9 / 9 = 1

1>1
• May 6th 2013, 01:24 PM
Plato
Re: Mathematical Induction help!!
Quote:

Originally Posted by zhengcl86
prove that for all n>1 , 10^n -1 is divisible by 9. Include both a basis step and an inductive step.

so for the basis step i have

let n =1 10(1) - 1 / 9
9 / 9 = 1

1>1

What is the inductive step?

Here is the trick:
$10^{N+1}-1=10^{N+1}-10+10-1=10{\color{blue}(10^N-1)}+9$
• May 6th 2013, 01:44 PM
zhengcl86
Re: Mathematical Induction help!!
so...10^1+1 - 1 = 10^1+1 - 10 + 10 -1 = 10(10^1 - 1) +9

10^2 - 1 = 10^2 - 10 + 10 - 1 = 10(9)+9
20-1 = 20-10+10-1 = 90+9
19 = 19 = 99
99???
• May 6th 2013, 01:50 PM
Plato
Re: Mathematical Induction help!!
Quote:

Originally Posted by zhengcl86
so...10^1+1 - 1 = 10^1+1 - 10 + 10 -1 = 10(10^1 - 1) +9

10^2 - 1 = 10^2 - 10 + 10 - 1 = 10(9)+9
20-1 = 20-10+10-1 = 90+9
19 = 19 = 99
99???

If you think that $10^2=20$ then you have absolutely no business even trying this question.

You don't even seem to have any idea what is meant by the inductive step. Do you?

Seek live help. We are not able to give you the sort of attention that you appear to need.
• May 6th 2013, 03:08 PM
zhengcl86
Re: Mathematical Induction help!!
so looked more into it lol, this is what i have,

10^k+1 -1 = 10^k 10^1 - 1
10^k-1 = 9q into 10^k = 9q+1
10^k+1 -1 = 10^k 10-1
(9q+1)10-1
90q+10-1
90q-9
9(10q+1)
and that has a factor of 9 so it is divisible
• May 6th 2013, 03:18 PM
Plato
Re: Mathematical Induction help!!
Quote:

Originally Posted by zhengcl86
so looked more into it lol, this is what i have,
10^k+1 -1 = 10^k 10^1 - 1
10^k-1 = 9q into 10^k = 9q+1
10^k+1 -1 = 10^k 10-1
(9q+1)10-1
90q+10-1
90q-9
9(10q+1)
and that has a factor of 9 so it is divisible

lol, you cannot possibly be serious about any of this.

None of that after the first line has any truth in fact.
You are truly challenged by very very basic algebra.

Please find some live help for yourself.
• May 6th 2013, 03:20 PM
zhengcl86
Re: Mathematical Induction help!!
lol..its what i went over in my notes, unless my professor is a re-re then there is no hope for me! thank you for your input.
• May 10th 2013, 01:48 AM
ibdutt
Re: Mathematical Induction help!!