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Let W be an infinite irreducible Coxeter group with (s_1, ..., s_n) thesimple generators. We give a simple proof that the word s_1 s_2 ... s_n s_1 s_2>... s_n ... s_1 s_2 ... s_n is reduced for any number of repetitions of s_1s_2 >... s_n. This result was proved for simply-laced, crystallographic groupsby Kleiner and Pelley using methods from the theory of quiver representations.Our proof only using basic facts about Coxeter groups and the geometry of rootsystems.

Powers of Coxeter elements in infinite groups are reduced