计算:1+11+2+11+2+3+…+11+2+3+…+100=______.-数学

题目简介

计算:1+11+2+11+2+3+…+11+2+3+…+100=______.-数学

题目详情

计算:1+
1
1+2
+
1
1+2+3
+…+
1
1+2+3+…+100
=______.
题型:填空题难度:中档来源:不详

答案

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

=1+class="stub"2
2
+(-class="stub"2
3
+class="stub"2
3
)+(-class="stub"2
4
+class="stub"2
4
)+(-class="stub"2
5
+class="stub"2
5
)+…+(-class="stub"2
100
+class="stub"2
100
)-class="stub"2
100+1

=1+class="stub"2
2
-class="stub"2
100+1

=2-class="stub"2
101

=1class="stub"99
101

故答案为1class="stub"99
101

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