化简

题目

化简
化简并求值 x=2 y=90
(x+y)+(2x+y/2)+(3x+y/2*3)+(4x+y/3*4)+.+(8x+y/8*9)
(x+y)+(2x+y/2)+(3x+y/2*3)+(4x+y/3*4)+....+(9x+y/8*9)
对不起 后面是9 ,打错了

答案

(x+y)+(2x+y/2)+(3x+y/2*3)+(4x+y/3*4)+.+(8x+y/8*9)
=(x+2x+3x+...+8x)+y[1+(1/2)+1/(2×3)+1/(3×4)+...+(1/(8×9)
=x(1+2+3+...+8)+y[1+(1/2)+(1/2-1/3)+(1/3-1/4)+.+
(1/8-1/9)]
=36x+y[1+1/2+1/2-1/9]
=36x+(17/9)y
x=2 y=90 时值=36×2+(17/9)×90=72+170=242