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
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