计算:12+13+23+14+24+34+15+25+35+…+1100+2100+…+99100.-数学

题目简介

计算:12+13+23+14+24+34+15+25+35+…+1100+2100+…+99100.-数学

题目详情

计算:
1
2
+
1
3
+
2
3
+
1
4
+
2
4
+
3
4
+
1
5
+
2
5
+
3
5
+…+
1
100
+
2
100
+…+
99
100
题型:解答题难度:中档来源:不详

答案

class="stub"1
2
+class="stub"1
3
+class="stub"2
3
+class="stub"1
4
+class="stub"2
4
+class="stub"3
4
+class="stub"1
5
+class="stub"2
5
+class="stub"3
5
+…+class="stub"1
100
+class="stub"2
100
+…+class="stub"99
100

=class="stub"1
2
+(class="stub"1
3
+class="stub"2
3
)+(class="stub"1
4
+class="stub"2
4
+class="stub"3
4
)+…+(class="stub"1
100
+class="stub"2
100
+…+class="stub"99
100

=class="stub"1
2
+class="stub"1
3
(1+2)×2
2
+class="stub"1
4
(1+3)×2
2
+…+class="stub"1
100
(1+99)×99
2

=class="stub"1
2
+class="stub"2
2
+class="stub"3
2
+class="stub"4
2
+…+class="stub"99
2

=class="stub"1
2
(1+99)×99
2

=2475.

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