12+56+1112+1920+2930+…+97019702+98999900.-数学

题目简介

12+56+1112+1920+2930+…+97019702+98999900.-数学

题目详情

1
2
+
5
6
+
11
12
+
19
20
+
29
30
+…+
9701
9702
+
9899
9900
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"29
30
+…+class="stub"9701
9702
+class="stub"9899
9900

=(1-class="stub"1
2
)+(1-class="stub"1
6
)+(1-class="stub"1
12
)+…+(1-class="stub"1
9900

=1×99-(class="stub"1
2
+class="stub"1
6
+class="stub"1
12
+…+class="stub"1
9900
),
=99-(class="stub"1
1×2
+class="stub"1
2×3
+class="stub"1
3×4
…+class="stub"1
99×100
),
=99-(1-class="stub"1
2
+class="stub"1
2
-class="stub"1
3
+class="stub"1
3
-class="stub"1
4
+…+class="stub"1
99
-class="stub"1
100
),
=99-(1-class="stub"1
100
),
=99-class="stub"99
100

=98class="stub"1
100

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