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Math Help - Geometric Series

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    Geometric Series

    Find a specific geometric series which sums to 30
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    Quote Originally Posted by thamathkid1729 View Post
    Find a specific geometric series which sums to 30
    Can you solve \dfrac{1}{1-r}=30~?
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    Thank you
    Is it possible to find a geometric series summing to -1/3?
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    A geometric series converges if and only if |r|<1.
    Apply my first reply.
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    So since r = 4, the answer is NO?
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    Quote Originally Posted by thamathkid1729 View Post
    Thank you
    Is it possible to find a geometric series summing to -1/3?
    \displaystyle -\left(\frac{1}{4} + \frac{1}{4^2} + \frac{1}{4^3} + ... \right) = -\frac{1}{3}
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    Can only rational numbers be sums of geometric series? Precisely which real numbers can be sums of geometric series?
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    Quote Originally Posted by thamathkid1729 View Post
    Can only rational numbers be sums of geometric series? Precisely which real numbers can be sums of geometric series?
    the sum can be any real number ... depends on the first term and the common ratio.
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    The series \sum_{n=0}^\infty ar^n sums to \frac{a}{1- r}. Whether that is a rational number or an irrational number depends upon a and r. For example, given any rational number, u, take a= 1 and solve \frac{1}{1- r}= u. Given any irrational number, v, take a= v/2 and a= 1/2.
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