题型:解决问题
题类:
难易度:普通
2022.10.12小学数学融侨南开六年级测试卷
阅读材料,完成下列问题:
对于由n个实数构成的数组A=(a
1 , a
2…… , a
n),以及任意给定的正整数
![](http://math.21cnjy.com/mml2svg?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Es%3C%2Fmi%3E%3C%2Fmath%3E)
, 我们定义:
![](http://math.21cnjy.com/mml2svg?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsubsup%3E%3Cmrow%3E%3Cmrow%3E%3Cmo%3E%E2%80%96%3C%2Fmo%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo%3E%E2%80%96%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi%3Es%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3C%2Fmrow%3E%3C%2Fmsubsup%3E%3Cmtext%3E%EF%BC%9D%3C%2Fmtext%3E%3Cmroot%3E%3Cmrow%3E%3Cmsubsup%3E%3Cmrow%3E%3Cmrow%3E%3Cmo%3E%7C%3C%2Fmo%3E%3Cmrow%3E%3Cmsubsup%3E%3Cmrow%3E%3Cmi%3Ea%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3C%2Fmrow%3E%3C%2Fmsubsup%3E%3C%2Fmrow%3E%3Cmo%3E%7C%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3Cmrow%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi%3Es%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmsubsup%3E%3Cmtext%3E%EF%BC%8B%3C%2Fmtext%3E%3Cmsubsup%3E%3Cmrow%3E%3Cmrow%3E%3Cmo%3E%7C%3C%2Fmo%3E%3Cmrow%3E%3Cmsubsup%3E%3Cmrow%3E%3Cmi%3Ea%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3C%2Fmrow%3E%3C%2Fmsubsup%3E%3C%2Fmrow%3E%3Cmo%3E%7C%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3Cmrow%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi%3Es%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmsubsup%3E%3Cmtext%3E%EF%BC%8B%3C%2Fmtext%3E%3Cmsubsup%3E%3Cmrow%3E%3Cmrow%3E%3Cmo%3E%7C%3C%2Fmo%3E%3Cmrow%3E%3Cmsubsup%3E%3Cmrow%3E%3Cmi%3Ea%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3C%2Fmrow%3E%3C%2Fmsubsup%3E%3C%2Fmrow%3E%3Cmo%3E%7C%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3Cmrow%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi%3Es%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmsubsup%3E%3Cmtext%3E%EF%BC%8B%3C%2Fmtext%3E%3Cmo%3E%E2%80%A6%3C%2Fmo%3E%3Cmo%3E%E2%80%A6%3C%2Fmo%3E%3Cmtext%3E%EF%BC%8B%3C%2Fmtext%3E%3Cmsubsup%3E%3Cmrow%3E%3Cmrow%3E%3Cmo%3E%7C%3C%2Fmo%3E%3Cmrow%3E%3Cmsubsup%3E%3Cmrow%3E%3Cmi%3Ea%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi%3En%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3C%2Fmrow%3E%3C%2Fmsubsup%3E%3C%2Fmrow%3E%3Cmo%3E%7C%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3Cmrow%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi%3Es%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmsubsup%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi%3Es%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmroot%3E%3C%2Fmath%3E)
。
例如:当
时,
。
(1)、当A=(1,2,……,2022)时,求
![](http://math.21cnjy.com/mml2svg?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsubsup%3E%3Cmrow%3E%3Cmrow%3E%3Cmo%3E%E2%80%96%3C%2Fmo%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo%3E%E2%80%96%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3C%2Fmrow%3E%3C%2Fmsubsup%3E%3C%2Fmath%3E)
。
(2)、当A=(x,y,z,w),已知
![](http://math.21cnjy.com/mml2svg?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsubsup%3E%3Cmrow%3E%3Cmrow%3E%3Cmo%3E%E2%80%96%3C%2Fmo%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo%3E%E2%80%96%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3C%2Fmrow%3E%3C%2Fmsubsup%3E%3Cmtext%3E%EF%BC%9D%3C%2Fmtext%3E%3Cmn%3E6%3C%2Fmn%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmath%3E)
, 令
![](http://math.21cnjy.com/mml2svg?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EB%3C%2Fmi%3E%3Cmtext%3E%EF%BC%9D%3C%2Fmtext%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmrow%3E%3Cmfrac%3E%3Cmrow%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E6%3C%2Fmn%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmtext%3E++%EF%BC%8C+%3C%2Fmtext%3E%3Cmfrac%3E%3Cmrow%3E%3Cmi%3Ey%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E6%3C%2Fmn%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmtext%3E++%EF%BC%8C+%3C%2Fmtext%3E%3Cmfrac%3E%3Cmrow%3E%3Cmi%3Ez%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E6%3C%2Fmn%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmn%3E%2C%3C%2Fmn%3E%3Cmfrac%3E%3Cmrow%3E%3Cmi%3Ew%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E6%3C%2Fmn%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
, 求
![](http://math.21cnjy.com/mml2svg?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsubsup%3E%3Cmrow%3E%3Cmrow%3E%3Cmo%3E%E2%80%96%3C%2Fmo%3E%3Cmrow%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo%3E%E2%80%96%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3C%2Fmrow%3E%3C%2Fmsubsup%3E%3C%2Fmath%3E)
。
(3)、若A=(x
1 , y
1),B=(x
2 , y
2),C=(x
1+x
2 , y
1+y
2),试比较
![](http://math.21cnjy.com/mml2svg?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsubsup%3E%3Cmrow%3E%3Cmrow%3E%3Cmo%3E%E2%80%96%3C%2Fmo%3E%3Cmrow%3E%3Cmi%3EA%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo%3E%E2%80%96%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3C%2Fmrow%3E%3C%2Fmsubsup%3E%3Cmtext%3E%EF%BC%8B%3C%2Fmtext%3E%3Cmsubsup%3E%3Cmrow%3E%3Cmrow%3E%3Cmo%3E%E2%80%96%3C%2Fmo%3E%3Cmrow%3E%3Cmi%3EB%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo%3E%E2%80%96%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3C%2Fmrow%3E%3C%2Fmsubsup%3E%3C%2Fmath%3E)
与
![](http://math.21cnjy.com/mml2svg?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsubsup%3E%3Cmrow%3E%3Cmrow%3E%3Cmo%3E%E2%80%96%3C%2Fmo%3E%3Cmrow%3E%3Cmi%3EC%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmo%3E%E2%80%96%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3C%2Fmrow%3E%3C%2Fmsubsup%3E%3C%2Fmath%3E)
的大小。