Consider the sequence \( \left \{ a_n \right \}_{n \in \mathbb{N}} \) defined by
\[\begin{align} a_1 &= \frac{3}{4} \\ a_n &= \frac{3^n}{4n} - \frac{3^{n-1}}{4 (n-1)}, n \in \mathbb{N} , n > 1 .\end{align} \]
What is the value of \( \displaystyle { \sum_{n=1}^{\infty} a_n } ?\)

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Consider the sequence \( \left \{ a_n \right \}_{n \in \mathbb{N}} \) defined by
\[\begin{align} a_1 &= 27 \\ a_n &= {(3n)}^{\frac{3}{n}}- {(3(n-1))}^{\frac{3}{n-1}}, n \in \mathbb{N} , n > 1 .\end{align} \]
What is the value of \( \displaystyle { \sum_{n=1}^{\infty} a_n } ?\)

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