9120+160+1120+1200+…+1900.-数学

题目简介

9120+160+1120+1200+…+1900.-数学

题目详情

9
1
20
+
1
60
+
1
120
+
1
200
+…+
1
900
题型:解答题难度:中档来源:不详

答案

class="stub"9
class="stub"1
20
+class="stub"1
60
+class="stub"1
120
+class="stub"1
200
+…+class="stub"1
900

=class="stub"9
class="stub"1
10
(class="stub"1
1×2
+class="stub"1
2×3
+class="stub"1
3×4
+class="stub"1
4×5
+…+class="stub"1
9×10
)

=class="stub"9
class="stub"1
10
×(1-class="stub"1
2
+class="stub"1
2
-class="stub"1
3
+class="stub"1
3
-class="stub"1
4
+…+class="stub"1
9
-class="stub"1
10
)

=class="stub"9
class="stub"1
10
×(1-class="stub"1
10
)

=class="stub"9
class="stub"1
10
×class="stub"9
10

=class="stub"9
class="stub"9
100

=100.

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