Geometric Progression

Question

The sum of the infinite GP 1/2, 1/4, 1/8, ... is

RankGuru · Accepted Answer

1. **Identify Terms**: $a = 1/2$. The common ratio $r = \frac{1/4}{1/2} = 1/2$.
2. **Convergence Condition**: Since $|r| < 1$, the sum to infinity exists.
3. **Sum Formula**: $S_{\infty} = \frac{a}{1 - r}$.
4. **Substitution**:
   - $S_{\infty} = \frac{1/2}{1 - 1/2} = \frac{1/2}{1/2}$.
5. **Result**: 1.

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