chứng tỏ rằng: S=1/1!+1/2!+1/3!+….+1/2019!<3

0 bình luận về “chứng tỏ rằng: S=1/1!+1/2!+1/3!+….+1/2019!<3”

1. `#Kenshiro`

   `S = 1/(1!) + 1/(2!) + 1/(3!) + … + 1/(2019!) < 3`

   Ta có : 

   `1/(2!) = 1/1.2`

   `1/(3!) = 1/2.3`

   `1/(2019!) = 1/2019.2020`

   `⇔ 1/1.2 + 1/2.3 + … + 1/2019.2020`

   `⇔ 1 – 1/2 + 1/2 – 1/3 + … + 1/2019 – 1/2020`

   `⇔ 1 – 1/2020 = 2019/2020`

   `⇒ 1 + 1/(1!) + 1/(2!) + 1/(3!) + … + 1/2020 < 1 ⇔ 1 + 1/(1!) + 1/(2!) + 1/(3!) + … + 1/2019 < 3`

   `⇒ S < 3`

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