Sequence and Series: JEE Main 2026 Mathematics question

Let $729, 81, 9, 1, \ldots$ be a sequence and $P_n$ denote the product of the first $n$ terms of this sequence. If $2\sum_{n=1}^{40} (P_n)^{\frac{1}{n}} = \frac{3^\alpha - 1}{3^\beta}$ and $\gcd(\alpha, \beta) = 1$, then $\alpha + \beta$ is equal to