化简（x+y）+(2x+y/1*2)+(3x+y/2*3)+...+(9x+y/8*9),并求当x=2,y=9时的值.

化简（x+y）+(2x+y/1*2)+(3x+y/2*3)+...+(9x+y/8*9),并求当x=2,y=9时的值.

（x+y）+(2x+y/1*2)+(3x+y/2*3)+...+(9x+y/8*9)
=(1+2+3+……+9)x+y(1+1-1/2+1/2-1/3+……+1/8-1/9)
=45x+y(2-1/9)
=45x+17/9y
=45×2+17/9×9
=90+17
=107