cho S = 1/5 mũ 2+ 1/6 mũ 2+……..+1/2020 mũ 2

0 bình luận về “cho S = 1/5 mũ 2+ 1/6 mũ 2+……..+1/2020 mũ 2”

1. Ta có:

   ` 1/5^2 < \frac{1}{4.5} `

   ` 1/6^2 < \frac{1}{5.6} `

   ` ……. `

   ` 1/2020^2 < \frac{1}{2019.2020} `

   ` => 1/5^2 + 1/6^2 + … + 1/2020^2 < \frac{1}{4.5} + \frac{1}{5.6} + … + \frac{1}{2019.2020} `

   ` => S < \frac{1}{4.5} + \frac{1}{5.6} + … + \frac{1}{2019.2020} `

   ` => S < 1/4 – 1/5 + 1/5 – 1/6 + … + 1/2019 . 1/2020 `

   ` => S < 1/4 – 1/2020 `

   Do: ` 1/4 – 1/2020 < 1/4 `

   ` => S < 1/4 ` (1)

   Ta có:

   ` 1/5^2 > \frac{1}{5.6} `

   ` 1/6^2 > \frac{1}{6.7} `

   ` ……….. `

   ` 1/2020^2 > \frac{1}{2020.2021} `

   ` => 1/5^2 + 1/6^2 + … + 1/2020^2 > \frac{1}{5.6} + \frac{1}{6.7} + … + \frac{1}{2020.2021} `

   ` => S > \frac{1}{5.6} + \frac{1}{6.7} + … + \frac{1}{2020.2021} `

   ` => S > 1/5 – 1/6 + 1/6 – 1/7 + … + 1/2020 – 1/2021 `

   ` => S > 1/5 – 1/2021 `

   Do: ` 1/5 – 2021 > 1/6 `

   ` => S > 1/6 ` (2) 

   Từ (1) và (2):

   ` => 1/6 < S < 1/4 ` ` (đpcm) `

   Trả lời

2. Cách làm

   ta thấy

   1/5^2<1/4.5

   1/6^2<1/5.6

   ……………………

   1/2020^2<1/2019.2020

   => 1/5^2+1/6^2+…+1/2020^2<1/4.5+1/5.6+1/2019.2020

   =1/4-1/5+1/5-1/6+…+1/2019-1/2020

   =1/4-1/2020

   lại có

   1/5^2>1/5.6

   1/6^2>1/6.7

   …………………….

   1/2020^2>1/2020.2021

   mk dang bận nên chỉ làm đc đến đây thôi chúc bạn học tốt

   Trả lời