Question

If a₁,a₂,..... are in A.P., then, \(\frac{1}{\sqrt{a_1} + \sqrt{a_2}} + \frac{1}{\sqrt{a_2} + \sqrt{a_3}} + .... + \frac{1}{\sqrt{a_n} + \sqrt{a_{n+1}}}\) is equal to

• A. \(\frac{n-1}{\sqrt{a_1}+\sqrt{a_{n-1}}}\)
• B. \(\frac{n}{\sqrt{a_1}+\sqrt{a_{n+1}}}\)
• C. \(\frac{n-1}{\sqrt{a_1}+\sqrt{a_{n}}}\)
• D. \(\frac{n}{\sqrt{a_1}-\sqrt{a_{n+1}}}\)

Answer 1

The Correct Option is B

Choose n = 1. The correct option should yield the first term i.e
1 / √a1 + √a2.
Only option (2) satisfies this condition.