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Question Number 157593 by metamorfose last updated on 25/Oct/21

let f:C→R            z→min(y−[y],[y+1]−y) , y=Im(z)  let w=e^(i((2π)/n)) , n∈N^∗   evaluate S_n =Σ_(0≤k<n) f(w^k )

$${let}\:{f}:{C}\rightarrow{R} \\ $$ $$\:\:\:\:\:\:\:\:\:\:{z}\rightarrow{min}\left({y}−\left[{y}\right],\left[{y}+\mathrm{1}\right]−{y}\right)\:,\:{y}={Im}\left({z}\right) \\ $$ $${let}\:{w}={e}^{{i}\frac{\mathrm{2}\pi}{{n}}} ,\:{n}\in{N}^{\ast} \\ $$ $${evaluate}\:{S}_{{n}} =\underset{\mathrm{0}\leqslant{k}<{n}} {\sum}{f}\left({w}^{{k}} \right) \\ $$

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