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[Community Question] Calculus: Limit of a power series

One of our user asked:

The series of functions $$ \sum_{n=0}^{+\infty} \frac{(-x)^n}{1+n!} $$ is pointwise convergent for any $x\in \mathbb{R}$, thus it defines a function $f:\mathbb{R}\rightarrow \mathbb{R}$. Is there a way to evaluate the limit $\lim_{x\rightarrow +\infty} f(x)$?


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