수학2_함수의 극한_자연상수 e의 정의_난이도 중

다음 극한값은? $\lim \limits_{n \to \infty} \left \{ \dfrac{1}{2} \left ( 1 + \dfrac{1}{n} \right ) \left ( 1 + \dfrac{1}{n+1} \right ) \left ( 1+ \dfrac{1}{n+2} \right ) \times \cdots \times \left (1+\dfrac{1}{2n} \right ) \right \}^{2n}$

 

① $\dfrac{1}{e^2}$          ② $\dfrac{1}{e}$          ③ $1$           ④ $e$          ⑤ $e^2$

 

 

정답 ④