If \( a_{1}, a_{2}, a_{3}, \ldots, a_{n} \in R^{+} \)and \( a_{1} \cdot a_{2} \cdot a_{3}, \ldot...

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If \( a_{1}, a_{2}, a_{3}, \ldots, a_{n} \in R^{+} \)and \( a_{1} \cdot a_{2} \cdot a_{3}, \ldots, a_{n}=1 \), then minimum value of \( \left(1+a_{1}+a_{1}^{2}\right)\left(1+a_{2}+a_{2}^{2}\right)\left(1+a_{3}+a_{3}^{2}\right) \) \( \ldots\left(1+a_{n}+a_{n}^{2}\right) \) is equal to.
(a) \( 3^{n+1} \)
(b) \( 3^{n} \)
(c) \( 3^{n-1} \)
(d) \( 3^{n-2} \)
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