$\\$
Đặt `A=1/5+1/5^2 + ... + 1/5^{98}+1/5^{99}`
`-> 1/5 A = 1/5^2 + 1/5^3 + ... + 1/5^{99}+1/5^{100}`
`-> A - 1/5A = (1/5+1/5^2 + ... + 1/5^{98}+1/5^{99})-( 1/5^2 + 1/5^3 + ... + 1/5^{99}+1/5^{100})`
`-> 4/5 A = 1/5 - 1/5^{100}`
`-> A = (1/5 - 1/5^{100}) . 5/4`
`-> A = 1/5 . 5/4 - 1/5^{100} . 5/4`
`-> A = 1/4 - 1/(5^{99} . 4) < 1/4`
`-> A < 1/4`
Hay `1/5+1/5^2 + ... + 1/5^{98}+1/5^{99} < 1/4`
