Question

lim

n→∞

(1-

1

22

)(1-

1

32

)(1-

1

42

)…(1-

1

n2

)=

 

．

Answer 1

分析：把求极限的式子利用平方差公式及约分化简得到

1

2

(1+

1

n

)对其求极限即可得到．

解答：解：

lim

n→∞

(1-

1

22

)(1-

1

32

)(1-

1

42

)(1-

1

n2

)
=

lim

n→∞

(1-

1

2

)(1+

1

2

)(1-

1

3

)(1+

1

3

)(1-

1

4

)(1+

1

4

)(1-

1

n

)(1+

1

n

)
=

lim

n→∞

1

2

(1+

1

n

)
=

1

2

．
故答案为

1

2

点评：本题考查学生认识函数的极限及运算的能力．