Ta có: `3/4! + 3/5! + 3/6! + ... + 3/100!`
`S=3/(1×2×3×4)+3/(1×2×3×4×5)+3/(1×2×3×4×5×6)+....3/(1×2×3×....×99×100)`
`S<3/(2×3)+3/(3×4)+3/(4×5)+ .......+3/(99×100)`
`S<3(1/(2×3)+1/(3×4)+1/(4×5)+ .......+1/(99×100))`
`S<3(1/2−1/3+1/3−1/4+1/4−.....−1/99+1/99−1/100)`
`S<3(1/2−1/100)`
`⇒S<3×49/100`
`⇒S<1/3!`