alleryThe sum to INFINITY of the GP $1 + 1/2 + 1/4 + 1/8 + \ldots$ is
A$1$
B$2$
C$4$
D$\infty$
Answer & Solution
Correct answer: B. $2$
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: syllabus Mathematics, Ch 8, §8.3 (Sum to infinity of GP), p. 7–8._
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