> 数学 >
计算:(1+
1
3
)(1+
1
8
)(1+
1
15
)…(1+
1
99
)=______.
人气:329 ℃ 时间:2019-09-27 06:57:42
解答
∵(1+
1
3
)=
4
3
=
22
22−1
;(1+
1
8
)=
9
8
=
32
32−1
;(1+
1
15
)=
42
42−1

∴(1+
1
3
)(1+
1
8
)(1+
1
15
)…(1+
1
99
)=
4
3
×
9
8
×
16
15
×
25
24
×
36
35
×
49
48
×
64
63
×
81
80
×…×
100
99
=
20
11
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