Floor Limit

Calculus Level 3

Let \(g(n) = n - \left \lfloor \frac{n}{2} \right \rfloor+ \left \lfloor \frac{n}{3} \right \rfloor - \left \lfloor \frac{n}{4} \right \rfloor + \cdots.\)

Evaluate \( \displaystyle \lim_{n \to \infty}\frac{g(n)}{n}.\)

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