Question 22.

$x_0 = 1$

$x_1 = 2$

$x_2 = \frac{1 + x_1}{x_0} = \frac{1 + 2}{1} = 3$

$x_3 = \frac{1 + x_2}{x_1} = \frac{1 + 3}{2} = 2$

$x_4 = \frac{1 + x_3}{x_2} = \frac{1 + 2}{3} = 1$

$x_5 = \frac{1 + x_4}{x_3} = \frac{1 + 1}{2} = 1$

$x_6 = \frac{1 + x_5}{x_4} = \frac{1 + 1}{1} = 2$

Hence, the series begins to repeat itself after every 5 terms.  

Terms whose number is of the form $5n$ are 1, $5n+1$ are 2, and so on, where $n = 0,1,2,3,\dots$

2021 is of the form $5n + 1$.  

Hence, its value will be 2.