数学试题讲解

(1)

lim_{n \to \infty} [\frac{1}{1 \times 2} + \frac{1}{2 \times 3} + \dots + \frac{1}{n (n + 1)}] = \underset{―}{}

.

(2)

lim_{n \to \infty} (\frac{n}{n^{2} + 1} + \frac{n}{n^{2} + 2} + \dots + \frac{n}{n^{2} + n}) = \underset{―}{}

.

(3)

lim_{n \to \infty} (\frac{1}{n + 1} + \frac{1}{n + 2} + \dots + \frac{1}{n + n}) = \underset{―}{}

.

(4)

lim_{n \to \infty} \sum_{i = 1}^{n} \frac{i}{n^{2}} e^{\frac{i}{n}} = \underset{―}{}