Question

[bla]

x/2.4+x/4.6+x/6.8+...+x/98.100=2

Answer 1

[𝔅𝔲̀𝔦 ℌ𝔬𝔞̀𝔫𝔤 𝔗𝔥𝔦𝔢̂𝔫 𝔏𝔞𝔪]

\(\dfrac{x}{2.4}+\dfrac{x}{4.6}+\dfrac{x}{6.8}+...+\dfrac{x}{98.100}=2\\ \Rightarrow x.\left(\dfrac{1}{2.4}+\dfrac{1}{4.6}+\dfrac{1}{6.8}+...+\dfrac{1}{98.100}\right)=2\\ \Rightarrow x.\left[\dfrac{1}{2}.\left(\dfrac{2}{2.4}+\dfrac{2}{4.6}+\dfrac{2}{6.8}+...+\dfrac{2}{98.100}\right)\right]=2\\ \Rightarrow x.\left[\dfrac{1}{2}.\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+...+\dfrac{1}{98}-\dfrac{1}{100}\right)\right]=2\Rightarrow x.\left[\dfrac{1}{2}.\left(\dfrac{1}{2}-\dfrac{1}{100}\right)\right]=2\\ \Rightarrow x.\left[\dfrac{1}{2}.\left(\dfrac{50}{100}-\dfrac{1}{100}\right)\right]=2\\ \Rightarrow x.\left[\dfrac{1}{2}.\dfrac{49}{100}\right]=2\\ \Rightarrow x.\dfrac{49}{200}=2\\ \Rightarrow x=2:\dfrac{49}{200}\\ \Rightarrow x=2.\dfrac{200}{49}\\ \Rightarrow x=\dfrac{400}{49}\)

Answer 2

[Lại DuyLâm]

x/2.4+x/4.6+...+x/98.100=2

<=>x(1/2.4+1/4.6+...+1/98.100)=2

<=>1/2x(1/2-1/4+1/4-1/6+...+1/98-1/100)=2

<=>1/2x(1/2-1/100)=2

<=>1/2x49/100=2

<=>49/200x=2

<=>x=400/49