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

Answer: (B)

$\frac{n}{\sqrt{a_1}+\sqrt{a_{n+1}}}$

Answer 2

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