We know that greater the value in the denominator compared to numerator , smaller will be the resulting number.
Based on the above statement we can eliminate options (B) and (C) when compared to other options.
For option (B) we get 1/4 + 1/16 + 1/36 + 1/64 will give you a number slightly greater than 1/4 (Between 1/4 and 1/2).
For option (C) we get 1/4+1/16+1/64+1/256 will give you a number slightly smaller than the option (B).
We are left out with three options (A) , (D) & (E).
In option (D) we are adding as well as subtracting the fractions mentioned.
(1-1/2)+(1/4-1/6) =1/2 + 1/12 which is almost equivalent to 0.6(0.5+0.1).
For answer option (E) we get
1/2+1/4+1/6+1/8 = 0.5 + 0.25 + 0.166 + 0.125 which will be greater than 1.
If your not able reduce the fraction 1/6 and 1/8 then from the first two no: itself we know that the no: is greater than 0.75 which is greater than the option (B) , (C) & (D).
Therefore currently option (E) is greatest.
Now we are left out with our final option (A) .
The option is similar to that of option (E) but the denominator is in square root form. We know that when the numerator is divided by the square root of a no: than the original no: it will yield a higher value .
For example : 1/4 = 0.25 is less than 1/[square root(4)] = 0.5 .
Considering the above analogy we can conclude that the greatest value which we can get among the options is (A).
Therefore option (A) is the answer.Hope the explanation helps