(x-1)÷2+(x-1)÷6+(x-1)÷12+···+(x-1)÷90=-3,求x的值

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(x-1)÷2+(x-1)÷6+(x-1)÷12+···+(x-1)÷90=-3,求x的值
(x-1)÷2+(x-1)÷6+(x-1)÷12+···+(x-1)÷90=-3,求x的值

(x-1)÷2+(x-1)÷6+(x-1)÷12+···+(x-1)÷90=-3,求x的值
(x-1)/1×2+(x-1)/2×3+……+(x-1)/9×10=-3
(x-1)(1-1/2+1/2-1/3+……+1/9-1/10)=-3
(x-1)(1-1/10)=-3
(x-1)(9/10)=-3
x-1=10/3
x=-7/3

(x-1)÷2+(x-1)÷6+(x-1)÷12+···+(x-1)÷90=-3
(x-1)×[1/2+1/(2x3)+1/(3x4)+……+1/(9x10)]=-3
(x-1)×﹙1-1/2+1/2-1/3+1/3-1/4+……+1/9-1/10)=-3
(x-1)×9/10=-3
3x-3=-10
3x=-7
x=-7/3

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