`( 1/3+1/6+1/12+1/24 +1/48+1/96) :y =21/2022 xx 32`
` ( 1/3+1/6+1/12+1/24 +1/48+1/96) :y = 112/337`
Đặt biểu thức là `A`
`A = 1/3+1/6+1/12+1/24 +1/48+1/96`
` => 2A = ( 1/3+1/6+1/12+1/24 +1/48+1/96)`
` => 2A = `\(\left(\dfrac{2}{3}+\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{24}+\dfrac{2}{48}+\dfrac{2}{96}\right)\)
`=> A = 2/3 + 1/3 + 1/6 + 1/12 + 1/24 + 1/48 + 1/96`
`=> 2A - A = 1/3 + 1/3 - 1/96`
` => 2A - A = 2/3 - 1/96`
` => 2A - A = 21/32`
Thay vào bài trên ta có:
` 21/32 : y = 112/337`
` y = 21/32 : 112/337`
` y = 1011/512`
\(\dfrac{\left(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{24}+\dfrac{1}{48}+\dfrac{1}{96}\right)}{y}=\dfrac{21}{2022}\times32\)
\(\Leftrightarrow\)\(\dfrac{\left(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{24}+\dfrac{1}{48}+\dfrac{1}{96}\right)}{y}=\dfrac{112}{337}\)
\(\Leftrightarrow112y=337\times\left(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{24}+\dfrac{1}{48}+\dfrac{1}{96}\right)\)
\(\Rightarrow y=\dfrac{\left(337\times\dfrac{21}{32}\right)}{112}=\dfrac{1011}{512}\)