Problem: Let $x_1=97$, and for $n>1$ let $x_n=\frac{n}{x_{n-1}}$. Calculate the product $x_1x_2 \ldots x_8$. Solution: Notice that for any odd $i > 1$, we have that $x_ix_{i+1} = x_i \cdot \frac{i+1}{x_i} = i+1$. Thus, we can write $ x_1x_2\ldots x_7x_8 = (x_1x_2)(x_3x_4)(x_5x_6)(x_7x_8) = 2 \cdot 4 \cdot 6 \cdot 8 = 384. .$