1/1*2x+1/2*3x+1/3*4x+1/4*5x+1/6*7x+1/7*8x+1/8*9x+1/9*10x=1/1

1/1*2x+1/2*3x+1/3*4x+1/4*5x+1/5*6x+1/6*7x+1/7*8x+1/8*9x+1/9*10x=1/10
1/(1*2)x+1/(2*3)x+1/(3*4)x+1/(4*5)x+1/(5*6)x+1/(6*7)x+1/(7*8)x+1/(8*9)x+1/(9*10)x=1/10
(1-1/2)x+(1/2-1/3)x+(1/3-1/4)x+(1/4-1/5)x+(1/5-1/6)x+(1/6-1/7)x+(1/7-1/8)x+(1/8-1/9)x+(1/9-1/10)x=1/10
(1-1/10)x=1/10
9/10x=1/10
x=1/9
1/1*2x+1/2*3x+1/3*4x+1/4*5x+1/5*6x+1/6*7x+1/7*8x+1/8*9x+1/9*10x=1/10
1/(1*2x)+1/(2*3x)+1/(3*4x)+1/(4*5x)+1/(5*6x)+1/(6*7x)+1/(7*8x)+1/(8*9x)+1/(9*10x)=1/10
(1-1/2)/x+(1/2-1/3)/x+(1/3-1/4)/x+(1/4-1/5)/x+(1/5-1/6)/x+(1/6-1/7)/x+(1/7-1/8)/x+(1/8-1/9)/x+(1/9-1/10)/x=1/10
(1-1/10)/x=1/10
(9/10)/x=1/10
9/10=(1/10)x
x=9
您在电脑上这样写题目会产生异议的,最好写上括号。1/5*6x这项一定漏写了吧。记住这个公式：1/(n*(n+1))=1/n-1/(n+1)。