Tham khảo
Đặt `A=1+\frac{1}{5}+\frac{1}{25}+...+\frac{1}{1953125}`
`⇒A=1+\frac{1}{5}+\frac{1}{5^2}+..+\frac{1}{5^9}`
`⇒\frac{1}{5}A=\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}+...+\frac{1}{5^{10}}`
`⇒A-\frac{1}{5}A=1+\frac{1}{5}+\frac{1}{5^2}+..+\frac{1}{5^9}-(\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}+...+\frac{1}{5^{10}})`
`⇒\frac{4}{5}A=1-\frac{1}{5^{10}}`
`⇒A=(1-\frac{1}{5^{10}}):\frac{4}{5}`
`⇒A=(1-\frac{1}{5^{10}}).\frac{5}{4}`
`⇒A=\frac{(5^{10}-1).5}{5^{10}.4}=\frac{5^{11}-5}{5^{10}.4}`
`\text{©CBT}`