题目内容
计算:(
+
+
+…+
)2+(
+
+
+…+
)×
-(1+
+
+…+
)×(
+
+…+
)=
1 |
2 |
2 |
3 |
3 |
4 |
9 |
10 |
1 |
2 |
2 |
3 |
3 |
4 |
9 |
10 |
1 |
2 |
1 |
2 |
2 |
3 |
9 |
10 |
2 |
3 |
3 |
4 |
9 |
10 |
考点:分数的巧算
专题:计算问题(巧算速算)
分析:通过观察,此题每个括号内的数字很接近,于是可通过设数法,进行简算.
解答:
解:设
+
+
+…+
=a,则:
(
+
+
+…+
)2+(
+
+
+…+
)×
-(1+
+
+…+
)×(
+
+…+
)
=a2+
a-(1+a)×(a-
)
=a2+
a-(a-
+a2-
a)
=a2+
a-a+
-a2+
a
=0
1 |
2 |
2 |
3 |
3 |
4 |
9 |
10 |
(
1 |
2 |
2 |
3 |
3 |
4 |
9 |
10 |
1 |
2 |
2 |
3 |
3 |
4 |
9 |
10 |
1 |
2 |
1 |
2 |
2 |
3 |
9 |
10 |
2 |
3 |
3 |
4 |
9 |
10 |
=a2+
1 |
2 |
1 |
2 |
=a2+
1 |
2 |
1 |
2 |
1 |
2 |
=a2+
1 |
2 |
1 |
2 |
1 |
2 |
=0
点评:对于此类问题,一般采取设数法,通过加减相互抵消,解决问题.
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