Results 1 to 2 of 2

Math Help - reciprocals

  1. #1
    Newbie
    Joined
    Nov 2007
    Posts
    13

    reciprocals

    Are there 21 different positive whole numbers such that the sum of their reciprocals is 1?

    I'm not sure about this question
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Dec 2007
    From
    Melbourne
    Posts
    428

    Yes

    Yes.

    1/2+1/3 = 5/6
     1/2+1/3+\frac{1/2+1/3}{6} = 35/36
     1/2+1/3+\frac{1/2+1/3}{6}+\frac{\frac{1/2+1/3}{6}}{6} = \frac{6^3-1}{6^3}

    We can keep doing this forever so the sum of any even number of reciprocals of natural numbers can represent \frac{6^n-1}{6^n}
    Adding a last number of 1/6^n produces 1, so the sum of any odd number of reciprocals of 1atural numbers can be 1
    Last edited by badgerigar; December 7th 2007 at 11:08 PM. Reason: forgot math tags
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Sum of reciprocals
    Posted in the Advanced Statistics Forum
    Replies: 9
    Last Post: January 30th 2010, 07:59 AM
  2. Sum of reciprocals of phi(p)
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: November 8th 2009, 03:49 PM
  3. The divergence of the reciprocals of odd integers
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: October 28th 2009, 05:30 PM
  4. Reciprocals
    Posted in the Algebra Forum
    Replies: 3
    Last Post: September 27th 2009, 05:29 PM
  5. Variable, reciprocals, and fractions..
    Posted in the Algebra Forum
    Replies: 3
    Last Post: July 20th 2005, 10:18 AM

Search Tags


/mathhelpforum @mathhelpforum