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Summation homework problem

  • #1
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Homework Statement



[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]

Homework Equations





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 .
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
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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:
 
  • #3
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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:
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 ?
 
  • #4
tiny-tim
Science Advisor
Homework Helper
25,832
250
(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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