grandes-ecoles 2018 Q15

grandes-ecoles · France · centrale-maths2__pc Sequences and series, recurrence and convergence Convergence proof and limit determination

Let $f$ be the function defined by $$f(x) = \sum_{n=1}^{+\infty} \left(\frac{1}{n+x} - \frac{1}{n}\right)$$ Let $k \in \mathbb{N}^{*}$. Using the result of Q14, deduce an asymptotic equivalent of $f$ at $-k$. What are the right and left limits of $f$ at $-k$?

Let $f$ be the function defined by
$$f(x) = \sum_{n=1}^{+\infty} \left(\frac{1}{n+x} - \frac{1}{n}\right)$$
Let $k \in \mathbb{N}^{*}$. Using the result of Q14, deduce an asymptotic equivalent of $f$ at $-k$. What are the right and left limits of $f$ at $-k$?

Paper Questions

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