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Math Help - A seemingly simple but really interesting problem

  1. #1
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    Joined
    Oct 2010
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    18

    A seemingly simple but really interesting problem

    What will be the value of the following expression (May be in fractional form)?
    0.7 + 7.7 + 0.777 + 7.777 + 0.77777 +  t_2_0

    I tried to solve the problem in the following way:
    0.7 + 7.7 + 0.777 + 7.777 + 0.77777 + t_2_0
    = 7/10 + 77/10 + 777/1000 + 7777/1000
    = [7/10 + 7 + 7/10] + [777/1000 + 7 + 777/1000]..
    = 7*10 + 2( 7/10 + 777/1000 + 77777/100000. t_1_0)
    Is this approach correct and if so how should I proceed? If not how shall I attack the problem?
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  2. #2
    Junior Member
    Joined
    Jul 2010
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    53
    Hello Rick,<br />
I think it should be somewhat like this.....<br /> <br />
  7{(1/10) + (11/10) + (111/1000) + (1111/1000) +..........to 20 terms)<br />
=(7/9){(9/10) + (99/10) + (999/1000) +.........................to 20 terms)<br />
=(7/9)[{(10-1)/10} + {(100-1)/10} + {(1000-1)/1000}+...to 20 terms)<br />
=(7/9)[ 1-(1/10)  + 10 - (1/10) +..................................to 20 terms)<br /> <br />
I think you can do it from here..............
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  3. #3
    Junior Member
    Joined
    Jul 2010
    Posts
    53
    Hello Rick,
    I think it should be somewhat like this.....

    7{(1/10) + (11/10) + (111/1000) + (1111/1000) +..........to 20 terms)<br />
=(7/9){(9/10) + (99/10) + (999/1000) +.........................to 20 terms)
    =(7/9)[{(10-1)/10} + {(100-1)/10} + {(1000-1)/1000}+...to 20 terms)<br />
=(7/9)[ 1-(1/10)  + 10 - (1/10) +..................................to 20 terms)
    I think you can do it from here..............
    Last edited by Arka; November 3rd 2010 at 09:08 PM. Reason: LATEX ERROR
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