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

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- May 6th 2013, 02:18 PMzhengcl86Mathematical 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, 02:24 PMPlatoRe: Mathematical Induction help!!
- May 6th 2013, 02:44 PMzhengcl86Re: 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, 02:50 PMPlatoRe: Mathematical Induction help!!
- May 6th 2013, 04:08 PMzhengcl86Re: 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, 04:18 PMPlatoRe: Mathematical Induction help!!
- May 6th 2013, 04:20 PMzhengcl86Re: 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, 02:48 AMibduttRe: Mathematical Induction help!!