Results 1 to 5 of 5

Math Help - mathematical induction problem

  1. #1
    Member
    Joined
    Aug 2008
    Posts
    249

    mathematical induction problem

    Use mathematical induction to prove the following:
    a factor of (9^n - 8n - 1) is 64 for all n > or = 2

    9^1 - 8 - 1 = 64a
    64 = 64a

    where a = any integer

    9^k - 8k - 1 = 64a

    prove that 9^(k+1) - 8(k+1) - 1 = 64b; where b = any integer
    9(9^k) - 8k - 9

    so that's how far i've gotten and now i'm stuck. please help me.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member arpitagarwal82's Avatar
    Joined
    Feb 2009
    Posts
    103
    First show that the statement is true for n = 2. Which infact is.

    Now assume

    9^k - 8k - 1 is true.

    Consider

    9^ (k + 1) - 8(k + 1) - 1

    Which is same as
    9 * 9^k - 8k - 9

    which on simplification gives 9 (9^k - 8k - 1) - 64k

    Now by assumption  9 (9^k - 8k - 1) is divisible by 64 and for k > 2 64k is divisible by 64.
    So statement is true for k + 1

    Hence proved.

    P.S I am new to this forum and am learning how to type mathematical expressions. So ignore any typing mistake.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,045
    Thanks
    886
    Quote Originally Posted by oblixps View Post
    Use mathematical induction to prove the following:
    a factor of (9^n - 8n - 1) is 64 for all n > or = 2

    9^1 - 8 - 1 = 64a
    64 = 64a

    where a = any integer

    9^k - 8k - 1 = 64a

    prove that 9^(k+1) - 8(k+1) - 1 = 64b; where b = any integer

    9(9^k) - 8k - 9
    9(9^k) - 9 - 8k

    9(9^k - 1) - 8k

    9(9^k - 8k - 1) - 8k + 9(8k)

    9(9^k - 8k - 1) + 8(8k)

    9(9^k - 8k - 1) + 64k

    9(64a) + 64k

    64(9a + k)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member arpitagarwal82's Avatar
    Joined
    Feb 2009
    Posts
    103
    Thanks skeeter. That was very clear way to explain. I went bit gross in my explanation.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Aug 2008
    Posts
    249
    thank you very much for the help guys!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Mathematical Induction problem
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: April 6th 2011, 12:52 PM
  2. Mathematical Induction Problem.
    Posted in the Differential Geometry Forum
    Replies: 14
    Last Post: June 9th 2010, 12:22 PM
  3. Mathematical Induction Problem!
    Posted in the Algebra Forum
    Replies: 2
    Last Post: April 15th 2010, 06:06 PM
  4. mathematical induction problem no.2
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: January 12th 2008, 08:45 PM
  5. mathematical induction problem
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: January 12th 2008, 08:22 PM

Search Tags


/mathhelpforum @mathhelpforum