计算下列式子的值:24×(12×3+14×5+…+120×21)-(112+112+22+…+112+22+…+102)-数学

题目简介

计算下列式子的值:24×(12×3+14×5+…+120×21)-(112+112+22+…+112+22+…+102)-数学

题目详情

计算下列式子的值:
24×(
1
2×3
+
1
4×5
+…+
1
20×21
)-(
1
12
+
1
12+22
+…+
1
12+22+…+102
题型:解答题难度:中档来源:不详

答案

24×(class="stub"1
2×3
+class="stub"1
4×5
+…+class="stub"1
20×21
)-(class="stub"1
12
+class="stub"1
12+22
+…+class="stub"1
12+22+…+102
),
=24×(class="stub"1
2×3
+class="stub"1
4×5
+…+class="stub"1
20×21
)-(class="stub"6
1×2×3
+class="stub"6
2×3×5
+…+class="stub"6
10×11×21
),
=6×[(class="stub"4
2×3
+class="stub"4
4×5
+…+class="stub"4
20×21
)-(class="stub"1
1×2×3
+class="stub"1
2×3×5
+…+class="stub"1
10×11×21
)],
=6×[class="stub"4
2×3
-class="stub"1
1×2×3
+class="stub"4
4×5
-class="stub"1
2×3×5
+…+class="stub"4
20×21
-class="stub"1
10×11×21
],
=6×[class="stub"1
1×2
+class="stub"1
2×3
+…+class="stub"1
10×11
],
=6×[1-class="stub"1
2
+class="stub"1
2
-class="stub"1
3
+…+class="stub"1
10
-class="stub"1
11
],
=6×class="stub"10
11

=class="stub"60
11

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