Question 108

# 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

Solution

We can see that the magnitude in each succeeding term is less than that of preceding term.

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.

Option A: $$\frac{2}{3}$$ < $$\frac{5}{6}$$. Hence, this can't be the answer.

Option B: $$\frac{2}{\sqrt{3}}$$ = 1.155 > $$1$$. Hence, this can't be the answer.

Option C: $$\sqrt{\frac{2}{3}}$$ = 0.8164 < $$\frac{5}{6}$$. Hence, this can't be the answer.

Option D: $$\frac{\sqrt{3}}{2}$$ = 0.866. This lies between (5/6, 1).Hence, this is the correct answer.