Tham khảo
`a) \frac{1}{28}+\frac{1}{36}+...+\frac{2}{x(x+1)}=\frac{4}{15}`
`⇒\frac{2}{56}+\frac{2}{72}+...+\frac{2}{x(x+1)}=\frac{4}{15}`
`⇒\frac{2}{7.8}+\frac{2}{8.9}+...+\frac{2}{x(x+1)}=\frac{4}{15}`
`⇒2.(\frac{1}{7.8}+\frac{1}{8.9}+...+\frac{1}{x(x+1)})=\frac{4}{15}`
Áp dụng `\frac{1}{n(n+1)}=\frac{1}{n}-\frac{1}{n+1}(n \ne 0,-1)`
`⇒\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+..+\frac{1}{x}-\frac{1}{x+1}=\frac{2}{15}`
`⇒\frac{1}{7}-\frac{1}{x+1}=\frac{2}{15}`
`⇒\frac{1}{x+1}=\frac{1}{105}`
`⇔x+1=105`
`⇒x=104`
Vậy `x=104`
`b) \frac{-9}{x}=\frac{x^2}{3}(x \ne 0)`
`⇒x.x^2=-9.3`
`⇒x^3=-27`
`⇒x^3=(-3)^3`
`⇒x=-3`
Vậy `x=-3`
`\text{©CBT}`
