$\\$
`A=1/5+1/5^2+...+1/5^{2016}`
`-> 1/5 A = 1/5^2+1/5^3+...+1/5^{2017}`
`->A-1/5A = (1/5+1/5^2+...+1/5^{2016})-(1/5^2+1/5^3+...+1/5^{2017})`
`-> 4/5 A = 1/5 - 1/5^{2017}`
`->A=(1/5 - 1/5^{2016}) . 5/4`
`->A = 1/4 - 1/(5^{2015} . 4) < 1/4`
`->A<1/4`