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If \( a_{1}, a_{2}, a_{3}, \ldots, a_{n} \) are in AP with \( a_{1}=0 \), prove that
\[
\begin{aligned}
\frac{a_{3}}{a_{2}}+\frac{a_{4}}{a_{3}}+\ldots+\frac{a_{n}}{a_{n-1}} & -a_{2}\left(\frac{1}{a_{2}}+\frac{1}{a_{3}}+\ldots+\frac{1}{a_{n-2}}\right) \\
& =\frac{a_{n-1}}{a_{2}}+\frac{a_{2}}{a_{n-1}}
\end{aligned}
\]
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