Question:
The sum of the first 15 terms of the series
\[
\frac{1}{24} + \frac{1}{104} + \frac{1}{234} + \dots = \frac{a}{b}, \text{ where HCF}(a,b) = 1. \text{ What is the difference between } a \text{ and } b?
\]
The sum of the first 15 terms of the series
\[
\frac{1}{24} + \frac{1}{104} + \frac{1}{234} + \dots = \frac{a}{b}, \text{ where HCF}(a,b) = 1. \text{ What is the difference between } a \text{ and } b?
\]
Show Hint
When calculating the sum of series, identify patterns and use formulas for series summation to simplify the process.
Updated On: Apr 17, 2025
- 59
- 67
- 73
- 78
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The Correct Option is C
Solution and Explanation
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.
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