tính tổng S= 1/2022 – 5/2.4 – 5/4.6 – 5/6.8 – …- 5/2020.2022

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1. `S = 1/2022 – ( 5/(2*4) + 5/(4*6) + 5/(6*8) + … +5/(2020*2022))`

   `Đặt A = 5/(2*4) + 5/(4*6) + 5/(6*8) +….+ 5/(2020*2022)`

   ` A/5 = 1/(2*4) + 1/(4*6) + 1/(6*8) +….+ 1/(2020*2022)`

   ` (2A)/5 = 2/(2*4) + 2/(4*6) + 2/(6*8) +….+ 2/(2020*2022)`

   ` (2A)/5 = 1/2-1/4+1/4-1/6+…+1/2020-1/2022`

   ` (2A)/5 = 1/2 – 1/2022`

   `(2A)/5 = 1010/2022= 505/1011`

   ` A = ((505/1011)*5)/2 `

   `A =2525/2022`

   `S = 1/2022 – 2525/2022 `

   `S = (-2524)/2022 = (-1262)/1011`

   `Chúc ngủ ngon!`

   `#KAITO#`

    

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2. S=$\frac{1}{2022}$- $\frac{5}{2.4}$- $\frac{5}{4.6}$-…- $\frac{5}{2020.2022}$ 

     =$\frac{1}{2022}$- ($\frac{5}{2.4}$+ $\frac{5}{4.6}$+…+ $\frac{5}{2020.2022}$ )

     =$\frac{1}{2022}$- $\frac{5}{2}$.($\frac{2}{2.4}$+ $\frac{2}{4.6}$+…+ $\frac{2}{2020.2022}$ )

     =$\frac{1}{2022}$- $\frac{5}{2}$.($\frac{1}{2}$-$\frac{1}{4}$+ $\frac{1}{4}$-$\frac{1}{6}$ +…+ $\frac{1}{2020}$-$\frac{1}{2022}$ )

     =$\frac{1}{2022}$- $\frac{5}{2}$.($\frac{1}{2}$-$\frac{1}{2022}$)

     =$\frac{1}{2022}$- $\frac{5}{2}$.$\frac{505}{1011}$

     =$\frac{1}{2022}$- $\frac{2525}{2022}$

     =$\frac{-1262}{1011}$ 

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