问题 填空题
lim
n→∞
(1-
1
22
)(1-
1
32
)(1-
1
42
)
(1-
1
n2
)
=______.
答案

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

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