Duration: 5:22

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Let \( D_{\mathrm{r}}=\left|\begin{array}{ccc}2^{\mathrm{r}-1} & 2.3^{\mathrm{r}-1} & 4.5^{\mathrm{r}-1} \\ \alpha & \beta & \gamma \\ 2^{\mathrm{n}}-1 & 3^{\mathrm{n}}-1 & 5^{\mathrm{n}}-1\end{array}\right| \). Then, the value of \( \sum_{\mathrm{r}=1}^{\mathrm{n}} D_{\mathrm{r}} \) is
A. \( \alpha \beta \gamma \)
B. \( 2^{\mathrm{n}} \alpha+3^{\mathrm{n}} \beta+4^{\mathrm{n}} \gamma \)
C. \( 2 \alpha+3 \beta+4 \gamma \)
D. None of these
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