A geometric series has a common ratio, $\displaystyle r=\frac{b-a}{b}$ , b>0. If 0<a<2b, show that the geometric series has a sum to infinity.
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Originally Posted by SengNee A geometric series has a common ratio, $\displaystyle r=\frac{b-a}{b}$ , b>0. If 0<a<2b, show that the geometric series has a sum to infinity. You need to show that -1 < r < 1: $\displaystyle 0 < a < 2b \Rightarrow \frac{b - 2b}{b} < \frac{b - a}{b} < \frac{b - 0}{b} \equiv -1 < \frac{b - a}{b} < 1 \equiv -1 < r < 1$.
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