The sum of $$1 - \frac{1}{6} + (\frac{1}{6} \times \frac{1}{4})-(\frac{1}{6} \times \frac{1}{4} \times \frac{5}{18})+$$ .... is
We can see that the magnitude in each succeeding term is less than that of preceding term.Â
Hence, we can say that for S = $$1 - \frac{1}{6} + (\frac{1}{6} \times \frac{1}{4})-(\frac{1}{6} \times \frac{1}{4} \times \frac{5}{18})+$$ ...
The value will lie between (5/6, 1). We can check with option choices.Â
Option A:Â $$\frac{2}{3}$$ <Â $$\frac{5}{6}$$. Hence, this can't be the answer.Â
Option B:Â $$\frac{2}{\sqrt{3}}$$ = 1.155 > $$1$$. Hence, this can't be the answer.Â
Option C:Â $$\sqrt{\frac{2}{3}}$$ = 0.8164 <Â $$\frac{5}{6}$$. Hence, this can't be the answer.Â
Option D: $$\frac{\sqrt{3}}{2}$$ = 0.866. This lies between (5/6, 1).Hence, this is the correct answer.Â
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