12×7+17×12+112×17+117×22+…+192×97+197×102=______.-数学

题目简介

12×7+17×12+112×17+117×22+…+192×97+197×102=______.-数学

题目详情

1
2×7
+
1
7×12
+
1
12×17
+
1
17×22
+…+
1
92×97
+
1
97×102
=______.
题型:解答题难度:中档来源:不详

答案

class="stub"1
2×7
+class="stub"1
7×12
+class="stub"1
12×17
+class="stub"1
17×22
+…+class="stub"1
92×97
+class="stub"1
97×102

=class="stub"1
5
×[(class="stub"1
2
-class="stub"1
7
)+(class="stub"1
7
-class="stub"1
12
)+(class="stub"1
12
-class="stub"1
17
)+(class="stub"1
17
-class="stub"1
22
)+…+(class="stub"1
92
-class="stub"1
97
)+(class="stub"1
97
-class="stub"1
102
)]
=class="stub"1
5
×[class="stub"1
2
-class="stub"1
102
]
=class="stub"1
5
×class="stub"25
51

=class="stub"5
51

故答案为:class="stub"5
51

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