Let $f$ be the function defined by $$f(x) = \sum_{n=1}^{+\infty} \left(\frac{1}{n+x} - \frac{1}{n}\right)$$ Using the result of Q12, deduce an asymptotic equivalent of $f$ at $+\infty$.
Let $f$ be the function defined by
$$f(x) = \sum_{n=1}^{+\infty} \left(\frac{1}{n+x} - \frac{1}{n}\right)$$
Using the result of Q12, deduce an asymptotic equivalent of $f$ at $+\infty$.