化简(x+y)+(2x+1*2分之1y)+(3x+2*3分之1y)+…+(9x+8*9分之1y);其中x=1,y=9

问题描述:

化简(x+y)+(2x+1*2分之1y)+(3x+2*3分之1y)+…+(9x+8*9分之1y);其中x=1,y=9

(x+y)+(2x+1*2分之1y)+(3x+2*3分之1y)+…+(9x+8*9分之1y)
=(x+2x+3x+...+9x)+(y+y/(1*2)+y/(2*3)+...+y/(8*9))
=45x+17y/9=62化简(x+y)+【2x+(1*2分之1)y】+【3x+(2*3分之1)y】+…+【9x+(8*9分之1)y】;其中x=1,y=9进行分组,分为x+2x+3x+...+9x=45x(等差数列)y+y/(1*2)+y/(2*3)+...+y/(8*9)=y(1+1/(1*2)+1/(2*3)+...+1/(8*9))=y(1+1/2-1/3+1/3-1/4+...1/8-1/9)=17y/9(裂项求和)