11×2+12×3+13×4+14×5+…+1199×200=______.-数学

题目简介

11×2+12×3+13×4+14×5+…+1199×200=______.-数学

题目详情

1
1×2
+
1
2×3
+
1
3×4
+
1
4×5
+…+
1
199×200
=______.
题型:解答题难度:中档来源:不详

答案

class="stub"1
1×2
+class="stub"1
2×3
+class="stub"1
3×4
+class="stub"1
4×5
+…+class="stub"1
199×200

=(class="stub"1
1
-class="stub"1
2
)+(class="stub"1
2
-class="stub"1
3
)+(class="stub"1
3
-class="stub"1
4
)+(class="stub"1
4
-class="stub"1
5
)+…+(class="stub"1
199
-class="stub"1
200

=1-class="stub"1
2
+class="stub"1
2
-class="stub"1
3
+class="stub"1
3
-class="stub"1
4
+class="stub"1
4
-class="stub"1
5
+…+class="stub"1
199
-class="stub"1
200

=1-class="stub"1
200

=class="stub"199
200

故答案为:class="stub"199
200

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