(x+y)+(2x+1/1*2y)+(3x+1/2*3y)+.+(9x+1/8*9y) 当X=2,Y=9时,求代数式的值
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(x+y)+(2x+1/1*2y)+(3x+1/2*3y)+.+(9x+1/8*9y) 当X=2,Y=9时,求代数式的值
![(x+y)+(2x+1/1*2y)+(3x+1/2*3y)+.+(9x+1/8*9y) 当X=2,Y=9时,求代数式的值](/uploads/image/z/2345253-69-3.jpg?t=%EF%BC%88x%2By%29%2B%282x%2B1%2F1%2A2y%29%2B%283x%2B1%2F2%2A3y%29%2B.%2B%289x%2B1%2F8%2A9y%29+%E5%BD%93X%3D2%2CY%3D9%E6%97%B6%2C%E6%B1%82%E4%BB%A3%E6%95%B0%E5%BC%8F%E7%9A%84%E5%80%BC)
(x+y)+(2x+1/1*2y)+(3x+1/2*3y)+.+(9x+1/8*9y)
= x(1+2+3+...9) + y { 1+1/(1*2)+1/(2*3)+1/(3*4)+...1/(8*9) }
= x(1+9)*9/2 + y { 1+1-1/2+1/2-1/3+1/3-1/4+...1/8-1/9) }
= 45x + y(2-1/9)
= 45x+2y-y/9
= 45*2 + 2*9 - 9/9
= 90+18-1
= 107
= x(1+2+3+...9) + y { 1+1/(1*2)+1/(2*3)+1/(3*4)+...1/(8*9) }
= x(1+9)*9/2 + y { 1+1-1/2+1/2-1/3+1/3-1/4+...1/8-1/9) }
= 45x + y(2-1/9)
= 45x+2y-y/9
= 45*2 + 2*9 - 9/9
= 90+18-1
= 107
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