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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 $\text{TRUE}$?

  1. The sequence $\{y_{n}\}$ does not have a limit as $n\rightarrow \infty$.
  2. $y_{n}\leq 1$ for all $\text{n} = 2,3,4, \dots$
  3. $\lim_{n\rightarrow \infty }y_{n}$ exists and is equal to $6/\pi ^{2}$.
  4. $\lim_{n\rightarrow \infty } y_{n}$ exists and is equal to $0$.
  5. The sequence $\{y_{n}\}$ first increases and then decreases as $\text{n}$ takes values $2, 3, 4, \dots$
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