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计算：11+(21-12)+(31-22+13)+(41-32+23-14)+…+(91-82+73-64+…+19)．-数学

题目简介

计算：11+(21-12)+(31-22+13)+(41-32+23-14)+…+(91-82+73-64+…+19)．-数学

题目详情

计算：
1
1
+(
2
1
-
1
2
)+(
3
1
-
2
2
+
1
3
)+(
4
1
-
3
2
+
2
3
-
1
4
)+…+(
9
1
-
8
2
+
7
3
-
6
4
+…+
1
9
)．
题型：解答题难度：中档来源：不详

答案

class="stub"1
1
+(class="stub"2
1
-class="stub"1
2
)+(class="stub"3
1
-class="stub"2
2
+class="stub"1
3
)+(class="stub"4
1
-class="stub"3
2
+class="stub"2
3
-class="stub"1
4
)+…+(class="stub"9
1
-class="stub"8
2
+class="stub"7
3
-class="stub"6
4
+…+class="stub"1
9
)，
=(class="stub"1
1
+class="stub"2
1
+class="stub"3
1
+class="stub"4
1
++class="stub"9
1
)-(class="stub"1
2
+class="stub"2
2
++class="stub"8
2
)+(class="stub"1
3
+class="stub"2
3
++class="stub"7
3
)-(class="stub"1
4
+class="stub"2
4
++class="stub"6
4
)+(class="stub"1
5
+class="stub"2
5
++class="stub"5
5
)-(class="stub"1
6
+class="stub"2
6
+class="stub"3
6
+class="stub"4
6
)+(class="stub"1
7
+class="stub"2
7
+class="stub"3
7
)-(class="stub"1
8
+class="stub"2
8
)+class="stub"1
9
，
=class="stub"9×10
2
-class="stub"1
2
×class="stub"8×9
2
+class="stub"1
3
×class="stub"7×8
2
-class="stub"1
4
×class="stub"6×7
2
+class="stub"1
5
×class="stub"5×6
2
-class="stub"1
6
×10+class="stub"6
7
-class="stub"3
8
+class="stub"1
9
，
=45-18+class="stub"28
3
-class="stub"21
4
+3-class="stub"5
3
+class="stub"6
7
-class="stub"3
8
+class="stub"1
9
，
=30+7class="stub"2
3
-5class="stub"1
4
+class="stub"6
7
-class="stub"3
8
+class="stub"1
9
，
=33class="stub"5
504
．

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