计算:(1-12-13-…-12003)(12+13+…+12004)-(1-12-13-…-12004)(12+13+…+12003)=______.-数学

题目简介

计算:(1-12-13-…-12003)(12+13+…+12004)-(1-12-13-…-12004)(12+13+…+12003)=______.-数学

题目详情

计算:(1-
1
2
-
1
3
-…-
1
2003
)(
1
2
+
1
3
+…+
1
2004
)-(1-
1
2
-
1
3
-…-
1
2004
)(
1
2
+
1
3
+…+
1
2003
)
=______.
题型:填空题难度:中档来源:不详

答案

class="stub"1
2
+class="stub"1
3
+…+class="stub"1
2004
=a

原式=(1-a+class="stub"1
2004
)×a-(1-a)×(a-class="stub"1
2004
),
=a-a2+class="stub"a
2004
-(a-a2-class="stub"1
2004
+class="stub"a
2004
),
=class="stub"1
2004

故答案为:class="stub"1
2004

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