Biomolecules, enzyme kinetics

### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2021 Q.30)** **1. Governing Concept & Definition**: - **Topic**: Engineering Mathematics & Infinite Geometric Series - The sum $S$ of an infinite geometric progression $a + ar + ar^2 + \dots$ with common ratio $|r| < 1$ is: $S = \frac{a}{1 - r}$ **2. Detailed Step-by-Step Calculation**: - **Given Series**: $S = 1 + \frac{1}{3} + \frac{1}{3^2} + \frac{1}{3^3} + \dots$ - First term $a = 1$ - Common ratio $r = \frac{1}{3} < 1$ - **Sum Evaluation**: $S = \frac{1}{1 - 1/3} = \frac{1}{2/3} = \frac{3}{2} = 1.5$ **3. Final Answer**: - **Calculated Value**: **1.5** - **Official GATE Accepted Range**: **1.5 to 1.5**