$\\$
`a,`
`C=1/5+1/5^2+...+1/5^{99}`
`->1/5 C = 1/5^2+1/5^3+...+1/5^{100}`
`->C-1/5 C=(1/5+1/5^2+...+1/5^{99})-(1/5^2+1/5^3+...+1/5^{100})`
`-> 4/5 C = 1/5 - 1/5^{100}`
`-> C=(1/5 - 1/5^{100}) . 5/4`
`->C = 1/4 - 1/(5^{99} . 4) < 1/4`
`->C<1/4` (Đpcm)
$\\$
`b,`
`D=3/(1^2 . 2^2)+5/(2^2 . 3^2)+...+19/(9^2 . 10^2)`
`->D=3/(1.4)+5/(4 . 9) + ... + 19/(81 . 100)`
`->D = 1 - 1/4 + 1/4 - 1/9 + ... + 1/81 - 1/100`
`->D=1-1/100 < 1`
`->D<1` (Đpcm)
