If \( a_{1}, a_{2}, \ldots \ldots a_{n} \) are in arithmetic progression, where \( a_{n}0 \) for...

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If \( a_{1}, a_{2}, \ldots \ldots a_{n} \) are in arithmetic progression, where \( a_{n}0 \) for all \( n \), show that :
\[
\frac{1}{\sqrt{a_{1}}+\sqrt{a_{2}}}+\frac{1}{\sqrt{a_{2}}+\sqrt{a_{3}}}+\ldots+\frac{1}{\sqrt{a_{n-1}}+\sqrt{a_{n}}}=\frac{n-1}{\sqrt{a_{1}}+\sqrt{a_{n}}} .
\]
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