Find the sum to infinity of the series $\frac{1}{4}$, $\frac{1}{8}$, $\frac{1}{16}$,..........

Analyze the question: The terms 1/4, 1/8, 1/16, ... form a geometric progression (GP), and we need the sum to infinity.

Concept: For a GP with first term a and common ratio r, where |r| < 1, the sum to infinity is:

S∞ = a / (1 − r)

Solution:

1. First term: a = 1/4
2. Common ratio: r = (1/8) ÷ (1/4) = 1/2. Check: (1/16) ÷ (1/8) = 1/2 ✓
3. Since |r| = 1/2 < 1, the sum to infinity exists.

S∞ = (1/4) / (1 − 1/2) = (1/4) / (1/2) = (1/4) × 2 = 1/2

Answer: Option A, 1/2.

Tip: Quick check: the series 1/2 + 1/4 + 1/8 + ... sums to 1. Our series is the same thing without the first term 1/2, so 1 − 1/2 = 1/2. Also, always confirm |r| < 1 before using a/(1 − r), since JAMB often includes distractors like negative or large values.