CBSE · Class 11 · Mathematics · Sequences and SeriesWhat is the sum of an infinite geometric series with first term $a = 1$ and common ratio $r = \frac{1}{2}$?
Step-by-Step Solution
The sum of an infinite geometric series is given by $S_\infty = \frac{a}{1 - r}$, provided $|r| < 1$. Here, $a = 1$ and $r = \frac{1}{2}$. Thus, $S_\infty = \frac{1}{1 - \frac{1}{2}} = \frac{1}{\frac{1}{2}} = 2$. Therefore, the correct option is B.
Detailed Options Breakdown
Option : 1
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Sequences and Series.
Option 1: 2 (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 2: 1/2
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Sequences and Series.
Option 3: Infinite
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Sequences and Series.
💡 Study Guide: This question tests core syllabus concepts from Sequences and Series. For formulas, key summaries, and mock exam reference guides, read the full Sequences and Series Revision Notes.