(1-12×2)×(1-13×3)×…×(1-110×10).-数学

题目简介

(1-12×2)×(1-13×3)×…×(1-110×10).-数学

题目详情

1-
1
2×2
)×(1-
1
3×3
)
×…×(1-
1
10×10
)
题型:解答题难度:中档来源:不详

答案

1-class="stub"1
2×2
)×(1-class="stub"1
3×3
)
×…×(1-class="stub"1
10×10
)

=class="stub"3
4
×class="stub"8
9
×…×class="stub"99
100

=class="stub"4
6
×class="stub"15
16
×…×class="stub"99
100

=class="stub"5
8
×class="stub"24
25
×…×class="stub"99
100

=…,
=class="stub"11
20

或者:原式=[(1+class="stub"1
2
)×(1-class="stub"1
2
)]×[(1+class="stub"1
3
)×(1-class="stub"1
3
)]×[(1+class="stub"1
4
)×(1-class="stub"1
4
)]×…×[(1+class="stub"1
10
)×(1-class="stub"1
10
)],
=class="stub"3
2
×class="stub"1
2
×class="stub"4
3
×class="stub"2
3
×class="stub"5
4
×class="stub"3
4
×…×class="stub"11
10
×class="stub"9
10

=class="stub"11
20

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