12+(14+34)+(16+36+56)+…+(1100+3100+5100+…+99100)=______.-数学

题目简介

12+(14+34)+(16+36+56)+…+(1100+3100+5100+…+99100)=______.-数学

题目详情

1
2
+(
1
4
+
3
4
)+(
1
6
+
3
6
+
5
6
)+…+(
1
100
+
3
100
+
5
100
+…+
99
100
)=______.
题型:填空题难度:中档来源:不详

答案

class="stub"1
2
+(class="stub"1
4
+class="stub"3
4
)+(class="stub"1
6
+class="stub"3
6
+class="stub"5
6
)+…+(class="stub"1
100
+class="stub"3
100
+class="stub"5
100
+…+class="stub"9
100
),
=class="stub"1
2
+class="stub"2
2
+class="stub"3
2
+…+class="stub"50
2

=class="stub"1
2
×(1+2+3+…+50),
=class="stub"1
2
×[(1+50)×50÷2],
=class="stub"1
2
×1275,
=637.5.
故答案为:637.5.

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