Find the limit of x_(n+1)/x_n if x_(n+1) = 1 - sqrt(1 - x_n) given that 0 <= x_1 < 1

One way would be to solve the recurrence relation x_(n+1) = 1 - sqrt(1 - x_n), given that 0 <= x_1 < 1, but I am not sure how to do this.

Hey lm1988.

Can you make a bound for 1 - sqrt(1 - x_n)? Also think about whether x_n is increasing or decreasing (if it decreases the limit should be towards the lower bound and if not it should be towards the upper bound).