3/4! + 3/5! + 3/6! + … + 3/100! < 1/3!

0 bình luận về “3/4! + 3/5! + 3/6! + … + 3/100! < 1/3!”

1. $#JAW#$

    

   Bình luận

2. 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!`

   Bình luận