（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
问题描述：
（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
答
（x+y)+(2x+1/1*2y)+(3x+1/2*3y)+......+(9x+1/8*9y)
=(x+2x+3x+...9x)+(y+1/1*2y+1/2*3y+1/8*9y)
=x(1+2+3+...+9)+y(1+1-1/2+1/2-1/3+1/3-1/4+...1/8-1/9)
=45x+ y(2-1/9)
=45*2+18-9/9
=107
答
（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