Câu hỏi 71
Cho hàm liên tục $f:[0,1]\to(0,\infty)$. Với $n\in\mathbb N$, $n\ge2$, xét $0=t_0\lt t_1\lt \dots\lt t_n=1$ sao cho
$$\int_{t_0}^{t_1}f(t)\,dt=\int_{t_1}^{t_2}f(t)\,dt=\dots=\int_{t_{n-1}}^{t_n}f(t)\,dt.$$
Tính
$$\lim_{n\to\infty}\frac{n}{\frac1{f(t_1)}+\frac1{f(t_2)}+\dots+\frac1{f(t_n)}}.$$
$$\int_{t_0}^{t_1}f(t)\,dt=\int_{t_1}^{t_2}f(t)\,dt=\dots=\int_{t_{n-1}}^{t_n}f(t)\,dt.$$
Tính
$$\lim_{n\to\infty}\frac{n}{\frac1{f(t_1)}+\frac1{f(t_2)}+\dots+\frac1{f(t_n)}}.$$