化简求值:(x+y)-(2x+1/2y)-(3x+1/6y)-(4x+1/12y)-(5x+1/20y)-......(10x+1/90y) ,其中x=1,y=
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解决时间 2021-02-27 09:55
- 提问者网友：活着好累
- 2021-02-26 20:20
化简求值:(x+y)-(2x+1/2y)-(3x+1/6y)-(4x+1/12y)-(5x+1/20y)-......(10x+1/90y) ,其中x=1,y=-2
最佳答案
- 五星知识达人网友：西风乍起
- 2021-02-26 20:26
(x+y)-(2x+1/2y)-(3x+1/6y)-(4x+1/12y)-(5x+1/20y)-......-(10x+1/90y)
=x+y-2x-1/2y--3x-1/6y-4x-1/12y-5x-1/20y-......-10x-1/90y
=x-2x-3x-4x-........-10x+y-1/2y-1/3y--...........-1/90y
=x-(2x+3x+4x+......+10x)+y-[1/(1*2)y+1/(2*3)y+1/(3*4)y+........+1/(9*10)y]
=x-(2x+10x)*9/2+y-y(1-1/2+1/2-1/3+1/3-1/4+........+1/9-1/10)
=x-54x+y-y*(1-1/10)
=-53x+y-y+1/10y
=-53x+1/10y追问x-(2x+10x)*9/2+y-y(1-1/2+1/2-1/3+1/3-1/4+........+1/9-1/10)
x-54x+y-y*(1-1/10)
没理解，说明一下吧追答1/2=1-1/2=1/(1*2)
1/6=1/2-1/3=1/(2*3)
.................
1/90=1/9-1/10=1/(9*10)追问x-(2x+10x)*9/2 没理解，也说明一下吧追答1+2+3+........+n=(n(n+1)/2
=x+y-2x-1/2y--3x-1/6y-4x-1/12y-5x-1/20y-......-10x-1/90y
=x-2x-3x-4x-........-10x+y-1/2y-1/3y--...........-1/90y
=x-(2x+3x+4x+......+10x)+y-[1/(1*2)y+1/(2*3)y+1/(3*4)y+........+1/(9*10)y]
=x-(2x+10x)*9/2+y-y(1-1/2+1/2-1/3+1/3-1/4+........+1/9-1/10)
=x-54x+y-y*(1-1/10)
=-53x+y-y+1/10y
=-53x+1/10y追问x-(2x+10x)*9/2+y-y(1-1/2+1/2-1/3+1/3-1/4+........+1/9-1/10)
x-54x+y-y*(1-1/10)
没理解，说明一下吧追答1/2=1-1/2=1/(1*2)
1/6=1/2-1/3=1/(2*3)
.................
1/90=1/9-1/10=1/(9*10)追问x-(2x+10x)*9/2 没理解，也说明一下吧追答1+2+3+........+n=(n(n+1)/2
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