In this question asked by S. Huntsman, he asks about an expression for the product: $$\prod_{k=1}^n (1-x^k)$$ Where the first answer made by Mariano Suárez-Álvarez states that given the Pentagonal Number Theorem, $$\prod_{n\geq1}(1-x^k) = \sum_{-\infty\leq n\leq\infty}(-1)^nx^{(3n^2-n)/2}$$ You can obtain the expression for the finite product, however, I am not able to see how to obtain this expression. My question is in the sense of knowing: How can I get an expression for the finite product from the pentagonal number theorem?

In this question asked by S. Huntsman, he asks about an expression for the product: $$\prod_{k=1}^n (1-x^k)$$ Where the first answer made by Mariano Suárez-Álvarez states that given the Pentagonal Number Theorem, $$\prod_{k\geq1}(1-x^k) = \sum_{-\infty\leq k\leq\infty}(-1)^kx^{(3k^2-k)/2}$$ You can obtain the expression for the finite product, however, I am not able to see how to obtain this expression. My question is in the sense of knowing: How can I get an expression for the finite product from the pentagonal number theorem?