The first few partial sums of a series consisting of only positive terms are shown. s Subscript 1 Baseline = one-fourth, s Subscript 2 baseline = StartFraction 5 Over 16 EndFraction, s Subscript 3 Baseline = StartFraction 21 Over 64 EndFraction, ellipsis

Based on this information, what would you conjecture the series converges to? Explain your reasoning.

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The fractional values appear to be getting larger. When converted to their decimal equivalents, the sums are 0.25, 0.3125, and 0.328125, respectively. Because the series converges, the partial sums must approach a specific value. That value is what the series converges to. It appears that these values are getting closer to 0.33, so the series might be converging to 0.33 or possibly .

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