grandes-ecoles 2018 Q17

grandes-ecoles · France · centrale-maths2__pc Sequences and Series Uniform or Pointwise Convergence of Function Series/Sequences

Let $f$ be the function defined by $$f(x) = \sum_{n=1}^{+\infty} \left(\frac{1}{n+x} - \frac{1}{n}\right)$$ Show that $f$ is of class $\mathcal{C}^{\infty}$ on $\mathcal{D}_{f}$ and calculate $f^{(k)}(x)$ for all $x \in \mathcal{D}_{f}$ and all $k \in \mathbb{N}^{*}$.

Let $f$ be the function defined by
$$f(x) = \sum_{n=1}^{+\infty} \left(\frac{1}{n+x} - \frac{1}{n}\right)$$
Show that $f$ is of class $\mathcal{C}^{\infty}$ on $\mathcal{D}_{f}$ and calculate $f^{(k)}(x)$ for all $x \in \mathcal{D}_{f}$ and all $k \in \mathbb{N}^{*}$.

Paper Questions

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