Question

The sum of the first 15 terms of the series \[ \frac{1}{24} + \frac{1}{104} + \frac{1}{234} + \dots = \frac{a}{b}, \text{ where HCF}(a,b) = 1. \text{ What is the difference between } a \text{ and } b? \]

• A. 59
• B. 67
• C. 73
• D. 78

Hint:

When calculating the sum of series, identify patterns and use formulas for series summation to simplify the process.

Answer 1

The Correct Option is C

The series appears to follow a pattern. Summing the first 15 terms and applying the formula for the sum of a series, we find the sum as a rational number \( \frac{a}{b} \), where the values of \( a \) and \( b \) satisfy the condition \( \text{HCF}(a, b) = 1 \). The difference between \( a \) and \( b \) is 73.