(1+12)×(1-12)×(1+13)×(1-13)×…×(1+1100)×(1-1100)-数学

题目简介

(1+12)×(1-12)×(1+13)×(1-13)×…×(1+1100)×(1-1100)-数学

题目详情

(1+
1
2
)×(1-
1
2
)×(1+
1
3
)×(1-
1
3
)×…×(1+
1
100
)×(1-
1
100
题型:解答题难度:中档来源:不详

答案

(1+class="stub"1
2
)×(1-class="stub"1
2
)×(1+class="stub"1
3
)×(1-class="stub"1
3
)×…×(1+class="stub"1
100
)×(1-class="stub"1
100

=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"101
100
×class="stub"99
100

=class="stub"1
2
×class="stub"3
2
×class="stub"2
3
×class="stub"4
3
×class="stub"3
4
×class="stub"5
4
×…×class="stub"99
100
×class="stub"101
100

=class="stub"1
2
×class="stub"101
100

=class="stub"101
200

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