The value of 1/4 + 1/(4 × 5) + 1/(4 × 5 × 6), correct to 4 decimal places, is:

Concept: For a sum built from a chain of unit fractions like 1/n + 1/(n × (n+1)) + 1/(n × (n+1) × (n+2)) + …, every term already contains the factor 1/n, since each later denominator is the previous one multiplied by the next integer. Pull that common factor 1/n out of every term first, then combine the simpler remaining fractions over one common denominator before doing any division — dividing only once, at the very end, avoids compounding rounding errors.

Application: Applying this to the given sum:

1. Factor 1/4 out of every term: 1/4 + 1/(4 × 5) + 1/(4 × 5 × 6) = (1/4) × [1 + 1/5 + 1/(5 × 6)].

2. Take the LCM of the denominators inside the bracket (1, 5, 30 → LCM 30): 1 + 1/5 + 1/30 = (30 + 6 + 1)/30 = 37/30.

3. Multiply back by the factored-out 1/4: (1/4) × (37/30) = 37/120.

4. Divide 37 by 120 to get the decimal, then round to four places: 37 ÷ 120 = 0.308333…, which rounds to 0.3083 (the digit after the fourth place is 3, below the rounding threshold, so the fourth-place digit stays unchanged).

Cross-check: Adding the three terms directly as decimals confirms it: 1/4 = 0.25, 1/20 = 0.05, and 1/120 = 0.008333…; summing gives 0.25 + 0.05 + 0.008333… = 0.308333…, the same figure obtained via the combined fraction — so the two methods agree.

Rounded to four decimal places, this matches the option showing 0.3083.