Results 1 to 8 of 8
Like Tree1Thanks
  • 1 Post By Plato

Math Help - Mathematical Induction help!!

  1. #1
    Junior Member
    Joined
    Feb 2013
    From
    New York
    Posts
    28

    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
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,824
    Thanks
    1717
    Awards
    1

    Re: Mathematical Induction help!!

    Quote Originally Posted by zhengcl86 View Post
    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
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2013
    From
    New York
    Posts
    28

    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???
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,824
    Thanks
    1717
    Awards
    1

    Re: Mathematical Induction help!!

    Quote Originally Posted by zhengcl86 View Post
    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.
    Thanks from Oldspice1212
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Feb 2013
    From
    New York
    Posts
    28

    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
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,824
    Thanks
    1717
    Awards
    1

    Re: Mathematical Induction help!!

    Quote Originally Posted by zhengcl86 View Post
    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.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    Feb 2013
    From
    New York
    Posts
    28

    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.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Super Member
    Joined
    Jul 2012
    From
    INDIA
    Posts
    831
    Thanks
    209

    Re: Mathematical Induction help!!

    Mathematical Induction help!!-mathematical-induction-10-may-13.png
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 10
    Last Post: June 29th 2010, 12:10 PM
  2. Mathematical Induction
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: May 6th 2010, 06:36 PM
  3. Mathematical induction
    Posted in the Algebra Forum
    Replies: 5
    Last Post: November 22nd 2008, 01:04 PM
  4. mathematical induction again
    Posted in the Algebra Forum
    Replies: 5
    Last Post: July 31st 2007, 04:34 AM
  5. Mathematical Induction
    Posted in the Algebra Forum
    Replies: 2
    Last Post: July 19th 2007, 11:14 AM

Search Tags


/mathhelpforum @mathhelpforum