Results 1 to 7 of 7

Math Help - Sum of series problem #1

  1. #1
    Senior Member
    Joined
    Feb 2008
    Posts
    383

    Sum of series problem #1

    did the first part

    how to do the next two part?

    {S}_{n}-\frac{1}{2}{S}_{n}= \frac{1}{2}+\frac{2}{4}+\frac{3}{8}+\frac{4}{16}+.  ..+\frac{n}{2^n}
                                                                                 -(\frac{1}{4}+\frac{2}{8}+\frac{3}{16}+...+\frac{n-1}{2^n}+\frac{n}{2^{n+1}})
                                             = \frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+.  ..+\frac{1}{2^n}-\frac{n}{2^{n+1}}



    Where did i go wrong?
    Attached Thumbnails Attached Thumbnails Sum of series problem #1-question_1.jpg  
    Last edited by BabyMilo; December 5th 2011 at 12:11 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28

    Re: Sum of series problem #1

    Here's a hint, have a look at the 2nd and 3rd last terms of S_n and \frac{1}{2}S_n
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Feb 2008
    Posts
    383

    Re: Sum of series problem #1

    Quote Originally Posted by pickslides View Post
    Here's a hint, have a look at the 2nd and 3rd last terms of S_n and \frac{1}{2}S_n
    i dont understand what you mean?

                                             =  \frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+.  ..+\frac{1}{2^n}-\frac{n}{2^{n+1}}

    where did i go wrong?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28

    Re: Sum of series problem #1

    \displaystyle S_n = \frac{1}{2}+\frac{2}{4}+\frac{3}{8}+\cdots +\frac{n-2}{2^{n-2}}+\frac{n-1}{2^{n-1}}+\frac{n}{2^n}

    Now do the same for \displaystyle\frac{1}{2}S_n
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member
    Joined
    Feb 2008
    Posts
    383

    Re: Sum of series problem #1

    Quote Originally Posted by pickslides View Post
    \displaystyle S_n = \frac{1}{2}+\frac{2}{4}+\frac{3}{8}+\cdots +\frac{n-2}{2^{n-2}}+\frac{n-1}{2^{n-1}}+\frac{n}{2^n}

    Now do the same for \displaystyle\frac{1}{2}S_n
     =(\frac{1}{4}+\frac{2}{8}+\frac{3}{16}+...+\frac{n-2}{2^{n-1}}+\frac{n-1}{2^n}+\frac{n}{2^{n+1}})
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28

    Re: Sum of series problem #1

    Now subtract like denominators at the end of the series.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Senior Member
    Joined
    Feb 2008
    Posts
    383

    Re: Sum of series problem #1

    Quote Originally Posted by pickslides View Post
    Now subtract like denominators at the end of the series.
                                             =  \frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+.  ..+\frac{1}{2^n}-\frac{n}{2^{n+1}}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Sum of series problem #2
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 5th 2011, 01:20 PM
  2. Replies: 3
    Last Post: September 29th 2010, 06:11 AM
  3. series problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 14th 2010, 11:22 PM
  4. Replies: 0
    Last Post: January 26th 2010, 08:06 AM
  5. series problem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 9th 2006, 07:23 PM

Search Tags


/mathhelpforum @mathhelpforum