Let \( \Delta_{r}=\left|\begin{array}{ccc}2^{r-1} & 2\left(3^{r-1}\right) & 4\left(5^{r-1}\right...

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Let \( \Delta_{r}=\left|\begin{array}{ccc}2^{r-1} & 2\left(3^{r-1}\right) & 4\left(5^{r-1}\right) \\ \alpha & \beta & \gamma \\ 2^{n}-1 & 3^{n}-1 & 5^{n}-1\end{array}\right| \) for \( r=1,2, \ldots \ldots \ldots \ldots \). The \( \sum_{r=1}^{n} \Delta_{r} \) is
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