Question

who can study the convergence of this suite
U0 from R+
U(n+1)=|Un²-1/4| n from N

Answer 1

please i want the anwser as far as possible

Answer 2

you can see for "large" U0
U1 will be larger than U0 e.g. let U0= 2
U1= 3.75
and U2 will be larger still.

on the other hand for a "small" U0, such as U0= 0.5
it looks like it converges.

we should solve for when
\[\bigg|x^2 - \frac{1}{4} \bigg| = x \]

Answer 3

thanks