Q:

Calculus Limit Calculation problem

The calculate the limit
$$\lim_{n \to \infty}\frac{1}{n}\left(\frac{n}{n+1}+\frac{n}{n+2}+...+\frac{n}{2n}\right).$$
Answer options: (A) ∞ (B) 0 (C) ln 2 (D) 1
I can just cancel the $1/n$ with each term within the big series. So, would the answer be zero?

A:

$$\lim_{n\to\infty}\sum_{1}^{n}\frac{1}{n+r}=\lim_{n\to\infty}\sum_{1}^{n}\frac{1/n}{1+r/n}=\int_0^1\frac{dx}{1+x}$$

