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    It may be shown that the sum from k=1 to infinity = lim n to infinity (r + r2 + r3 + ... rn ) = r/(1-r) for any lrl<1. Use this fact to write the following recurring decimal in rational form p/q where p and q are whole numbers.

    0.161616161616....

    Thanks :confused:
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    (Original post by *Sarah...*)
    It may be shown that the sum from k=1 to infinity = lim n to infinity (r + r2 + r3 + ... rn ) = r/(1-r) for any lrl<1. Use this fact to write the following recurring decimal in rational form p/q where p and q are whole numbers.

    0.161616161616....

    Thanks :confused:
    I'm not sure what method they are talking about but it can be done like this
    Let x = 0.16161616...*****(1)
    Then 100x = 16.161616****(2)
    (2) - (1)
    99x =16
    x=16/99
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    (Original post by steve2005)
    I'm not sure what method they are talking about but it can be done like this
    Let x = 0.16161616...*****(1)
    Then 100x = 16.161616****(2)
    (2) - (1)
    99x =16
    x=16/99
    oh thanks for that, I didn't realise it was so simple
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    Oh thanks for that i didn't realise it was so simple!
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    (Original post by *Sarah...*)
    Oh thanks for that i didn't realise it was so simple!
    Yes, steve's fraction is correct BUT the question says use a particular method... I don't think steve has used this method so ' no marks'

    I don't know the method either. We need Gaz or AlphaNumeric to put us on the right path.

    Edit: I've used the required method.

    0.1616161616 = 16/100 + 16/10000 + 16/1000000....
    This is a GP with r= 1/100
    r/(1-r) = [16/100]/[1- 1/100]=[16/100]/[99/100] =16/99
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    (Original post by carol05)
    Yes, steve's fraction is correct BUT the question says use a particular method... I don't think steve has used this method so ' no marks'

    I don't know the method either. We need Gaz or AlphaNumeric to put us on the right path.

    Edit: I've used the required method.

    0.1616161616 = 16/100 + 16/10000 + 16/1000000....
    This is a GP with r= 1/100
    r/(1-r) = [16/100]/[1- 1/100]=[16/100]/[99/100] =16/99
    Yes, I think this fulfills the requirements of the question. I always prefer it when the question says. Hence, or otherwise...... this then allows you to use any method, although the one suggested is often the easiest..
 
 
 
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