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If \( a, a_{1}, a_{2}, a_{3}, \ldots, a_{2 n}, b \) are in A.P. and \( a, g_{1}, g_{2}, g_{3}, \ldots \) \( g_{2 n}, b \) are in G.P. and \( h \) is the H.M. of \( a \) and \( b \), then prove that
\[
\frac{a_{1}+a_{2 n}}{g_{1} g_{2 n}}+\frac{a_{2}+a_{2 n-1}}{g_{2} g_{2 n-1}}+\cdots+\frac{a_{n}+a_{n+1}}{g_{n} g_{n+1}}=\frac{2 n}{h}
\]
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