On the Series ${\sum }_{n=0}^{\mathrm{\infty }}{t}^n{f}^{(n)}(t)(-1{)}^n\mathrm{/}n!$

We study the series ${\sum }_{n=0}^{\mathrm{\infty }}\frac{(-1{)}^n}{n!}{t}^n{f}^{(n)}(t)$. We show that for analytic functions this series is uniformly and absolutely convergent to the constant $f(0)$. We show that there are nowhere analytic functions for them the series is divergent for all $t$ and also there are nowhere analytic functions for them the series is convergent to $f(0)$ at least for $t$ in a dense subset of $\mathbb{R}$.