Results 1 to 2 of 2

Math Help - infinite sum

  1. #1
    Member
    Joined
    Jun 2009
    Posts
    77

    infinite sum

    the infinite sum 1+ 4/7 + 9/7^2 +16/7^3 + 25/7^4 + ...... equals?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jan 2009
    Posts
    715
    I prefer to use techniques of differentiation :

         \frac{1^1}{7^0} + \frac{2^2}{7} +  \frac{3^2}{7^2} + \frac{4^2}{7^3} + ...


    Consider

      \frac{1}{1-x} = 1 + x + x^2 + x^3 + x^4 + ....


    Take differential ,

      \frac{1}{(1-x)^2} = 1 + 2x + 3x^2 + 4x^3 + ..   ~~~~~      -[1]

    Take it agian ,

      \frac{2}{(1-x)^3} = 2 + 3(2) x + 4(3) x^2 + ...   ~~~~~        -[2]

     [1] + x  [2]

      \frac{1}{(1-x)^2} + \frac{2x}{(1-x)^3} = 1 + (2+2)x + (3+3(2))x^2 + (4 + 4(3))x^3 + ...

      = 1+2^2x + 3^2x^2 + 4^2 x^3 + ....


    Sub .  x = \frac{1}{7}

      \frac{1^1}{7^0} + \frac{2^2}{7} +  \frac{3^2}{7^2} + \frac{4^2}{7^3} + ...  = \frac{1}{(1-1/7)^2} + \frac{2/7}{(1-1/7)^3}

      = \frac{49}{36} + \frac{49}{108}

      = \frac{49}{27}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: December 5th 2011, 11:47 PM
  2. Replies: 1
    Last Post: October 2nd 2011, 02:26 AM
  3. Replies: 7
    Last Post: October 12th 2009, 10:10 AM
  4. Prove: every set with an infinite subset is infinite
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: March 31st 2009, 04:22 PM
  5. Proof: infinite set minus a fintie set is infinite
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: February 24th 2009, 10:54 PM

Search Tags


/mathhelpforum @mathhelpforum