u is a real parameter such that 0<u<1.
For 0≤x≤u, f(x)=0.
For u≤x≤n, f(x)=1−(ux+(1−u)(1−x))2.
The sequence {un} is define recursively as follows: u1=f(1) and un=f(un−1) ∀n∈N,n=1.
Show that there exists a positive integer k for which uk=0. parameterizationtrigonometryalgebra unsolvedalgebra