u_(n+1) = u_n −u_n ^3 ; u_0 ∈ ]0, 1[ . show that u_n ∈ ]0, 1[ . show that u_n converges to 0 v_n = (1/u_(n+1) ^2 ) − (1/u_n ^2 ) . express v_n interms of u_n . show that v_n converges to 2 f(x) = ((2−x)/((1−x)^2 )) . show that f is increasing and deduce that v_n is decreasing . show that v_n ≥ 2