12+56+1112+1920+…+379380=______.-数学

题目简介

12+56+1112+1920+…+379380=______.-数学

题目详情

1
2
+
5
6
+
11
12
+
19
20
+…+
379
380
=______.
题型:解答题难度:中档来源:不详

答案

class="stub"1
2
+class="stub"5
6
+class="stub"11
12
+class="stub"19
20
+…+class="stub"379
380

=(1-class="stub"1
2
)+(1-class="stub"1
6
)+(1-class="stub"1
12
)+(1-class="stub"1
20
)+…+(1-class="stub"1
380
),
=19-(class="stub"1
2
+class="stub"1
6
+class="stub"1
12
+class="stub"1
20
+…+class="stub"1
380
),
=19-(1-class="stub"1
2
+class="stub"1
2
-class="stub"1
3
+class="stub"1
3
-class="stub"1
4
+…+class="stub"1
19
-class="stub"1
20
),
=19-1+class="stub"1
20

=18class="stub"1
20

故答案为:18class="stub"1
20

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