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!`