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  1. #1
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    Exclamation G.P.

    Show that there are 3 geometrical progression in which the second term is - 4/3 and the sum of the first three terms is 28/9. SHow that one of these series is convergent and, in this case, find the limit of its sum.

    How on EARTH do i do this question???

    x - 4/3 + y = 28/9...
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  2. #2
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    Quote Originally Posted by Sunyata View Post
    Show that there are 3 geometrical progression in which the second term is - 4/3 and the sum of the first three terms is 28/9. SHow that one of these series is convergent and, in this case, find the limit of its sum.

    How on EARTH do i do this question???

    x - 4/3 + y = 28/9...
    Since this is a geometric progression, you know that t_{n + 1} = rt_n.

    Therefore r = \frac{t_{n + 1}}{t_n}.


    So here r = \frac{-\frac{4}{3}}{x} and r = \frac{y}{-\frac{4}{3}}.

    Therefore \frac{-\frac{4}{3}}{x} = \frac{y}{-\frac{4}{3}}

    y = \frac{-\frac{4}{3}\left(-\frac{4}{3}\right)}{x}

    y = \frac{\frac{16}{9}}{x}

    y = \frac{16}{9x}.


    Therefore, the sum of the first three terms is

    x - \frac{4}{3} + \frac{16}{9x} = \frac{28}{9}.

    Solve for x and then you can find y.
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  3. #3
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    What does it mean by convergent?
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  4. #4
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    It means that if you had an infinite number of terms, if you were to add them up, you would find that the sum tends to a number, rather than tending to \infty.
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