bài 2 : Tìm x x/2022 – 1/10 – 1/15 – 1/21 – …. – 1/120 = 5/8

2 bình luận về “bài 2 : Tìm x x/2022 – 1/10 – 1/15 – 1/21 – …. – 1/120 = 5/8”

1. ${\displaystyle \frac{x}{2022}}–{\displaystyle \frac{1}{10}}–{\displaystyle \frac{1}{15}}-{\displaystyle \frac{1}{21}}–\dots .–{\displaystyle \frac{1}{120}}={\displaystyle \frac{5}{8}}$

   $<=>{\displaystyle \frac{x}{2020}}-2({\displaystyle \frac{1}{20}}+{\displaystyle \frac{1}{30}}+{\displaystyle \frac{1}{41}}+\dots +{\displaystyle \frac{1}{240}})={\displaystyle \frac{5}{8}}$

   $<=>x:2020-2.({\displaystyle \frac{1}{4}}-{\displaystyle \frac{1}{5}}+{\displaystyle \frac{1}{5}}-{\displaystyle \frac{1}{6}}+\dots +{\displaystyle \frac{1}{15}}-{\displaystyle \frac{1}{16}})={\displaystyle \frac{5}{8}}$

   $<=>x:2020-2.{\displaystyle \frac{3}{16}}={\displaystyle \frac{5}{8}}$

   $<=>x:2020=1$

   $<=>x=2020$

   Trả lời
2. x/2022 – 1/10 – 1/15 – 1/21 – …. – 1/120 = 5/8

   <=> x/2022 – (1/10 + 1/15 + 1/21 + ….+ 1/120) = 5/8

   Đặt 1/10 + 1/15 + 1/21 + ….+ 1/120 = A 

   Ta có: A = 1/10+ 1/15+1/21+…+1/120 

                 = 2/20+2/30+2/42+…+2/240

                 =2/(4xx5)+2/(5xx6)+…..+2/(15xx16)

                 = 2xx[1/(4xx5)+1/(5xx6)+………..+ 1/(15xx16)]

                 = 2xx [ 1/4-1/5+1/5-1/6+………+1/15-1/16]

                 = 2xx[1/4-1/16]

                = 2xx3/16

                 = 3/8

   thay vào ta có : 

   x/2022 – 3/8 = 5/8

   <=> x/2022 = 1

   <=> x/2022 = 2022/2022

   <=> x = 2022

   Trả lời