6. A sequence of positive integers \(u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots\) is defined by \(\left\{ \begin{array} { c } u _ { 1 } = 1
u _ { n + 1 } = 3 u _ { n } + 2 \end{array} ( n \geq 1 ) \right.\)
Prove by induction that \(u _ { n } = 2 \left( 3 ^ { n - 1 } \right) - 1\).
(4)
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