Question

If $a_1, a_2, a_3, a_4$ are in A.P., then $\frac{1}{\sqrt{a_1} + \sqrt{a_2}} + \frac{1}{\sqrt{a_2} + \sqrt{a_3}} + \frac{1}{\sqrt{a_3} + \sqrt{a_4}} =$

• A. \( \frac{\sqrt{a_4} - \sqrt{a_1}}{a_3 - a_2} \)
• B. \( \frac{a_4 - a_1}{a_3 - a_2} \)
• C. \( \frac{a_3 - a_2}{\sqrt{a_4} - \sqrt{a_1}} \)
• D. \( \frac{a_1 - a_4}{a_3 - a_1} \)
• E. \( \frac{a_5 - a_0}{a_1 - a_4} \)

Hint:

This type of sum is a "telescoping series." When you rationalize the denominators of terms involving consecutive A.P. elements, most terms in the middle will cancel out, leaving only parts of the first and last terms.

Answer 1

The Correct Option is A