Maths Paper 1, November 2024, question 1.3

Look at the product $(1+\frac{1}{3})(1+\frac{1}{4})(1+\frac{1}{5})\dots (1+\frac{1}{n})$, where $n\ge 3$ and the last factor is $1+\frac{1}{n}$. Find ALL the values of $n$ for which this product is a whole number.