question_answer

If \[{{a}_{r}}>0,\] \[r\in N\] and \[{{a}_{1}},\,{{a}_{2}},\,{{a}_{3}},.......{{a}_{2n}}\] are in AP, then \[\frac{{{a}_{1}}+{{a}_{2n}}}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{2}}}}+\frac{{{a}_{2}}+{{a}_{2n-1}}}{\sqrt{{{a}_{2}}}+\sqrt{{{a}_{3}}}}+\frac{{{a}_{3}}+{{a}_{2n-2}}}{\sqrt{{{a}_{3}}}+\sqrt{{{a}_{4}}}}+......+\frac{{{a}_{n}}+{{a}_{n+1}}}{\sqrt{{{a}_{n}}}+\sqrt{{{a}_{n+1}}}}\] is equal

A)  \[n-1\]              

B)  \[\frac{n({{a}_{1}}+{{a}_{2n}})}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{n+1}}}}\]

C)  \[\frac{n-1}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{n+1}}}}\]               

D)  \[\frac{n+1}{\sqrt{{{a}_{1}}+{{a}_{n}}}}\]

E)  None of these