Consider the sequence
$$y_{n}=\frac{1}{\int_{1}^{n}\frac{1}{\left ( 1+x/n \right )^{3}}dx}$$
for $\text{n} = 2,3,4, \dots$ Which of the following is $\text{TRUE}$?
- The sequence $\{y_{n}\}$ does not have a limit as $n\rightarrow \infty$.
- $y_{n}\leq 1$ for all $\text{n} = 2,3,4, \dots$
- $\lim_{n\rightarrow \infty }y_{n}$ exists and is equal to $6/\pi ^{2}$.
- $\lim_{n\rightarrow \infty } y_{n}$ exists and is equal to $0$.
- The sequence $\{y_{n}\}$ first increases and then decreases as $\text{n}$ takes values $2, 3, 4, \dots$