The aim of this paper is to present some sequences of Euler type. We will explore the sequences \left( F_{n}\right) _{n\geq 1}, defined by F_{n}\left( x\right) =\sum_{k=1}^{n}f\left( k\right) -\int_{1}^{n+x}f\left(t\right) dt, for any n\geq 1 and x\in \left[ 0,1\right] , where f is a local integrable and positive function defined on \left[ 1,\infty \right). Starting from some particular example we will find that this sequence is uniformly convergent to a constant function. Also, we present a stability result.

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 Marinescu, Dan Ştefan, Monea, Mihai