GATE BT 2015 • Q33
NAT • 1 Mark
Section 2: General Biotechnology
Biomolecules, enzyme kinetics
Subtopic: Fundamentals of Biomolecules, enzyme kinetics
Question Statement:
Consider the following infinite series:
1+r+r2+13+..........00
If r = 0.3, then the sum of this infinite series is
1.40 to 1.43
Official Answer Key:
1.40 to 1.43
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2015 Q.33)**
**1. Governing Concept & Definition**:
- **Topic**: Engineering Mathematics & Sum of Infinite Geometric Series
- For $|r| < 1$:
$S = 1 + r + r^2 + r^3 + \dots = \frac{1}{1 - r}$
**2. Detailed Step-by-Step Calculation**:
- **Given**:
- $r = 0.3 < 1$
- **Sum**:
$S = \frac{1}{1 - 0.3} = \frac{1}{0.7} = \frac{10}{7} \approx 1.42857 \approx 1.43$
**3. Final Answer**:
- **Calculated Value**: **1.43**
- **Official GATE Accepted Range**: **1.40 to 1.43**
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