Question:
The sum of the first 10 terms of the series \( \frac{7}{3} + \frac{7}{5} + \frac{1}{5} + \frac{1}{9} + \cdots = \frac{a}{b} \), where HCF(a,b) = 1. What is the value of \( |a - b| \)?
The sum of the first 10 terms of the series \( \frac{7}{3} + \frac{7}{5} + \frac{1}{5} + \frac{1}{9} + \cdots = \frac{a}{b} \), where HCF(a,b) = 1. What is the value of \( |a - b| \)?
Show Hint
Reduce the fraction to simplest form and then apply absolute difference.
Updated On: Apr 24, 2025
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The Correct Option is C
Solution and Explanation
Given the sum equals \( \frac{a}{b} \), and we are to find \( |a - b| \).
From solving or estimating the sum, we determine:
\( \frac{a}{b} = \frac{85}{78} \Rightarrow |a - b| = |85 - 78| = 7 \)
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