Question

The sum of the first 10 terms of the series \[ \frac{7}{3} + \frac{7}{15} + \frac{1}{5} + \frac{1}{9} + \dots \quad \text{where} \quad \text{HCF}(a,b) = 1. \] What is the value of \( |a - b| \)?

• A. 5
• B. 6
• C. 7
• D. 9

Hint:

When solving series, break down the individual terms and look for patterns or simplifications to help determine the final sum.

Answer 1

The Correct Option is C

The sum of the series is given as: \[ S = \frac{7}{3} + \frac{7}{15} + \frac{1}{5} + \frac{1}{9} + \dots \] Here, the HCF of \( a \) and \( b \) is given to be 1. By calculating the sum of the terms and solving for \( |a - b| \), we get the result as \( 7 \).