Let $\ z_n$ be a sequence. There exists $\ m <> k$ with $\ m\geq 1$ and $\ k\leq\dfrac{n}{3}$ so that $\ z_m= \dfrac{{a_m}{z_m}+{a_k}{z_k}}{3}$, where the complex numbers of the sequence $\ a_n$ all have the module equal to 1. Study the convergence of the sequence defined by the sum of all modules of $\ z_n$. I am unable to find how to use the module of complex numbers here. Should I use the fact that $\ |m+n|<=|m|+|n|$? At least for the boundedness? How to solve it?
2026-03-25 07:44:52.1774424692
Study the convergence of the sequence defined by the sum of all modules of $\ z_n$.
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