若代数式1/2(x+1)+1/6(x+1)+1/12(x+1)+.+1/90(x+1)的值为18,求x的值在线等哦

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若代数式1/2(x+1)+1/6(x+1)+1/12(x+1)+.+1/90(x+1)的值为18,求x的值在线等哦
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若代数式1/2(x+1)+1/6(x+1)+1/12(x+1)+.+1/90(x+1)的值为18,求x的值在线等哦
若代数式1/2(x+1)+1/6(x+1)+1/12(x+1)+.+1/90(x+1)的值为18,求x的值
在线等哦

若代数式1/2(x+1)+1/6(x+1)+1/12(x+1)+.+1/90(x+1)的值为18,求x的值在线等哦
1/2(x + 1) + 1/6(x + 1) + 1/12(x + 1)+ ...+1 /90(x + 1) = 18
(x + 1) (1/2 + 1/6 + 1/12 + ...+ 1/90) = 18
(x + 1) (1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ...+ 1/9 - 1/10) = 18
(x + 1) (1 - 1/10) = 18
(x + 1) (9/10) = 18
x + 1 = 20
x = 19

原方程左边
=(x+1)*(1/2+1/6+1/12+....1/90)
=(x+1)*(1/(1*2)+1/(2*3)+1/(3*4)+....+1/(9*10))
=(x+1)*(1-1/10)
=(x+1)*9/10
=18
故x=19