If \[{{a}_{1}},\ {{a}_{2}},\ {{a}_{3}}.......{{a}_{n}}\] are in A.P., where \[{{a}_{i}}>0\] for all \[i\], then the value of\[\frac{1}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{2}}}}+\frac{1}{\sqrt{{{a}_{2}}}+\sqrt{{{a}_{3}}}}+\] \[........+\frac{1}{\sqrt{{{a}_{n-1}}}+\sqrt{{{a}_{n}}}}=\] [IIT 1982]

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

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

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

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

If \[{{a}_{1}},\ {{a}_{2}},\ {{a}_{3}}.......{{a}_{n}}\] are in A.P.,

1.	If \[{{a}_{1}},\ {{a}_{2}},\ {{a}_{3}}.......{{a}_{n}}\] are in A.P., where \[{{a}_{i}}>0\] for all \[i\], then the value of\[\frac{1}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{2}}}}+\frac{1}{\sqrt{{{a}_{2}}}+\sqrt{{{a}_{3}}}}+\] \[........+\frac{1}{\sqrt{{{a}_{n-1}}}+\sqrt{{{a}_{n}}}}=\] [IIT 1982]
A.	\[\frac{n-1}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{n}}}}\]
B.	\[\frac{n+1}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{n}}}}\]
C.	\[\frac{n-1}{\sqrt{{{a}_{1}}}-\sqrt{{{a}_{n}}}}\]
D.	\[\frac{n+1}{\sqrt{{{a}_{1}}}-\sqrt{{{a}_{n}}}}\]
Answer» B. \[\frac{n+1}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{n}}}}\]

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If \[{{a}_{1}},\ {{a}_{2}},\ {{a}_{3}}.......{{a}_{n}}\] are in A.P., where \[{{a}_{i}}>0\] for all \[i\], then the value of\[\frac{1}{\sqrt{{{a}_{1}}}+\sqrt{{{a}_{2}}}}+\frac{1}{\sqrt{{{a}_{2}}}+\sqrt{{{a}_{3}}}}+\] \[........+\frac{1}{\sqrt{{{a}_{n-1}}}+\sqrt{{{a}_{n}}}}=\] [IIT 1982]

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