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Math Help - Sum to infinity

  1. #1
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    Sum to infinity

    The sum to infinity of a geometric progression is 5 and the sum to infinity of another series formed by taking the first, fourth, seventh, tenth, ... terms (that is, U1+U4+U7+U10+...) is 4. Find the common ratio of the first series.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Hint

    The ratio of the second series is the cube of the first one.
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  3. #3
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    Quote Originally Posted by FernandoRevilla View Post
    Hint

    The ratio of the second series is the cube of the first one.
    sorry but why is this so?
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  4. #4
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    Quote Originally Posted by Punch View Post
    sorry but why is this so?
    Write the first series out: a + ar + ar^2 + ar^3 + ar^4 + ar^5 + ar^6 + ....

    Now take the first, fourth, seventh, tenth etc. terms and draw the conclusion that was pointed out to you in post #2.
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