`C=1/5 + 1/5^2 + 1/5^3 +...+1/5^2017`
`1/5 C= 1/5 ( 1/5 +1/5^2 + 1/5^3+...+1/5^2017)`
`1/5C = 1/5^2 + 1/5^3 + 1/5^4 +...+ 1/5^2018`
`C- 1/5 C= 1/5 + 1/5^2 + 1/5^3 +...+1/5^2017 - 1/5^2 - 1/5^3 - 1/5^4-..-1/5^2018`
`4/5 C = 1/5 - 1/5^2018`
`C= (1/5 - 1/5^2018):4/5`
`C= (1/5- 1/5^2018) . 5/4`
`C = 1/4 - 1/(5^2017 .4) < 1/4`
Vậy `C < 1/4`