Question 11
(ROM 6) Find all solutions $(x_1,x_2,\ldots,x_n)$ of the equation
$$1+\frac1{x_1}+\frac{x_1+1}{x_1x_2}+\frac{(x_1+1)(x_2+1)}{x_1x_2x_3}+\cdots+\frac{(x_1+1)\cdots(x_{n-1}+1)}{x_1x_2\cdots x_n}=0.$$
$$1+\frac1{x_1}+\frac{x_1+1}{x_1x_2}+\frac{(x_1+1)(x_2+1)}{x_1x_2x_3}+\cdots+\frac{(x_1+1)\cdots(x_{n-1}+1)}{x_1x_2\cdots x_n}=0.$$