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Math Help - Sum to infinity

  1. #1
    Member SengNee's Avatar
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    Sum to infinity

    A geometric series has a common ratio, r=\frac{b-a}{b} , b>0.
    If 0<a<2b, show that the geometric series has a sum to infinity.
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  2. #2
    Flow Master
    mr fantastic's Avatar
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    Quote Originally Posted by SengNee View Post
    A geometric series has a common ratio, r=\frac{b-a}{b} , b>0.
    If 0<a<2b, show that the geometric series has a sum to infinity.
    You need to show that -1 < r < 1:

    0 < a < 2b \Rightarrow \frac{b - 2b}{b} < \frac{b - a}{b} < \frac{b - 0}{b} \equiv -1 < \frac{b - a}{b} < 1 \equiv -1 < r < 1.
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