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. $\dfrac{x}{2022} – \dfrac{1}{10} – \dfrac{1}{15} -\dfrac{ 1}{21} – …. – \dfrac{1}{120} =\dfrac{ 5}{8}$

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

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

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

   $<=>x:2020=1$

   $<=>x=2020$

   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