`A = 1/5+1/5^2+1/5^3+.....+1/5^2008`
`=> 5.A = 5(1/5 + 1/5^2 +1/5^3+.....+1/5^2008 )`
`=> 5.A = 1+ 1/5 + ... + 1/5^2007`
`=> 5.A - A =( 1+ 1/5 + ... + 1/5^2007) - ( 1/5 + ... + 1/5^2008 )`
`=> 4A = 1 - 1/5^2008`
`=> A = 1 - 1/5^2008 : 4`
`=> A = 1/4 - 1/(5^2008 . 4) < 1/4`
`=> A < 1/4`