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Summation homework problem

  1. Mar 9, 2010 #1
    1. The problem statement, all variables and given/known data

    [tex]\sum^{n}_{r=1}(\lg \frac{2^r(r+1)}{r})=\sum^{n}_{r=1}[\lg 2^r+\lg (r+1)-\lg r][/tex]

    2. Relevant equations



    3. The attempt at a solution

    i found the answer to be [tex](2^n-1)\lg 2 +\lg (n+1)[/tex]

    Am i correct , or it can be further simplified ? Thanks .
     
  2. jcsd
  3. Mar 9, 2010 #2

    tiny-tim

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    Hi thereddevils! :smile:

    Your lg(n+1) is fine, but the two-y part isn't …

    how did you manage to get a 2n outside the lg ? :wink:
     
  4. Mar 9, 2010 #3
    Re: summation

    Thanks , tiny tim !

    oh , \sum^{n}_{r=1}\lg 2^r=\lg 2+2\lg 2+3\lg 2 +...

    =\lg 2 (1+2+3+...)

    =\frac{n}{2}(n+1)\lg 2

    i think i see my mistake , is this correct ?
     
  5. Mar 9, 2010 #4

    tiny-tim

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    (have a sigma: ∑ and try using the X2 tag just above the Reply box :wink:)

    Yes, that's all correct now! :smile:
     
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