Question 161
Two sequences of real numbers are defined as follows:
$$
u_1 = 0, \quad u_{n+1} = \frac{1}{2}(u_n + v_n)$$
$$v_1 = 1, \quad v_{n+1} = \frac{1}{4}(u_n + 3v_n)$$
Find the value of $v_{2016} - u_{2016}$.
$$
u_1 = 0, \quad u_{n+1} = \frac{1}{2}(u_n + v_n)$$
$$v_1 = 1, \quad v_{n+1} = \frac{1}{4}(u_n + 3v_n)$$
Find the value of $v_{2016} - u_{2016}$.