化简:1/xy+1/(x+4)(y+4)+1/(x+8)(y+8)+1/(x+12)(y+12)+.1/(x+4n)(y+4n) n为整数

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/25 09:07:28
化简:1/xy+1/(x+4)(y+4)+1/(x+8)(y+8)+1/(x+12)(y+12)+.1/(x+4n)(y+4n)n为整数化简:1/xy+1/(x+4)(y+4)+1/(x+8)(y+8

化简:1/xy+1/(x+4)(y+4)+1/(x+8)(y+8)+1/(x+12)(y+12)+.1/(x+4n)(y+4n) n为整数
化简:1/xy+1/(x+4)(y+4)+1/(x+8)(y+8)+1/(x+12)(y+12)+.1/(x+4n)(y+4n) n为整数

化简:1/xy+1/(x+4)(y+4)+1/(x+8)(y+8)+1/(x+12)(y+12)+.1/(x+4n)(y+4n) n为整数
1/xy=(1/x-1/y)*(1/y-x)
1/(x+4)(y+4)=(1/(x+4)-1/(y+4))*(1/y-x)
.以此推类
提取(1/y-x) 原式=( 1/y-x)*(1/x-1/y+1/(x+4)-1/(y+4).1/(x+4n)-1/(y+4n))
因为x=4,y=8
所以 原式=(1/4)*( 1/4 -1/8+1/8 -1/12.1/(4+4n) -1/(8+4n))
=(1/4)*(1/4-1/(8+4n))
=(n+1)/(32+16n)
希望能给你点思路
也希望给我点分.

应该可以列项化简.