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

Question

If $$a_1, a_2, ......$$ 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

Accepted Answer

n a 1 + a n + 1 \frac{n}{\sqrt{a_1} + \sqrt{a_{n + 1}}} a 1 ​ ​ + a n + 1 ​ ​ n ​. We have, 1 a 1 + a 2 + 1 a 2 + a 3 + . . . . . . . + 1 a n + a n + 1 \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}}} a 1 ​ ​ + a 2 ​ ​ 1 ​ + a 2 ​ ​ + a 3 ​ ​ 1 ​ + ....... + a n ​ ​ + a n + 1 ​ ​ 1 ​ Now, 1 a 1 + a 2 \frac{1}

If $a_1, a_2, ......$ 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

If $a_1, a_2, ......$ 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