I have no idea what to do here:
The sequence (u_n) is defined by u_0 = 0 and \(u_n = \dfrac{1}{2 + u_{n - 1}}\)
Compute u_5.
+23246 u0 = 0
un = 1 / ( 2 + un-1 )
We'll have to work our way up from u0 to u5.
u1 = 1 / ( 2 + u0 ) ---> u1 = 1 / ( 2 + 0 ) = 1/2
u2 = 1 / ( 2 + u1 ) ---> u2 = 1 / ( 2 + 1/2 ) = 2/5
u3 = 1 / ( 2 + u2 ) ---> u3 = 1 / ( 2 + 2/5 ) = 5/12
u4 = 1 / ( 2 + u3 ) ---> u4 = 1 / ( 2 + 5/12 ) = 12/29
u5 = 1 / ( 2 + u4 ) ---> u5 = 1 / ( 2 + 12/29 ) = .............
