计算:16+112+120+130+142+156+172+19012+14+18+…+1128+1256.-数学

题目简介

计算:16+112+120+130+142+156+172+19012+14+18+…+1128+1256.-数学

题目详情

计算:
1
6
+
1
12
+
1
20
+
1
30
+
1
42
+
1
56
+
1
72
+
1
90

1
2
+
1
4
+
1
8
+…+
1
128
+
1
256
题型:解答题难度:中档来源:不详

答案

class="stub"1
6
+class="stub"1
12
+class="stub"1
20
+class="stub"1
30
+class="stub"1
42
+class="stub"1
56
+class="stub"1
72
+class="stub"1
90

=class="stub"1
2×3
+class="stub"1
3×4
+class="stub"1
4×5
+class="stub"1
5×6
+class="stub"1
6×7
+class="stub"1
7×8
+class="stub"1
8×9
+class="stub"1
9×10

=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"1
2
-class="stub"1
10

=class="stub"2
5


class="stub"1
2
+class="stub"1
4
+class="stub"1
8
+…+class="stub"1
128
+class="stub"1
256

=(1-class="stub"1
2
)+(class="stub"1
2
-class="stub"1
4
)+(class="stub"1
4
-class="stub"1
8
)+…+(class="stub"1
128
-class="stub"1
256
),
=1-class="stub"1
256

=class="stub"255
256

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