The sum to INFINITY of the GP $1 + 1/2 + 1/4 + 1/8 + \ldots$ is

1. Infinite GP sum formula (when $|r| < 1$): $S_\infty = \dfrac{a}{1 - r}$. 2. For this series, first term $a = 1$, common ratio $r = 1/2$. 3. $S_\infty = \dfrac{1}{1 - 1/2} = \dfrac{1}{1/2} = 2$. 4. Sanity check by partial sums: $1 = 1$, $1+1/2 = 1.5$, $1+1/2+1/4 = 1.75$, $1+1/2+1/4+1/8 = 1.875$, approaching 2. ✓ 5. Option A is just the first term. Option C doubles the answer. Option D ignores that $|r| < 1$ keeps the sum finite. _Source: NCERT Class 11 Mathematics, Ch 8, §8.3 (Sum to infinity of GP), p. 7–8._