Question

Tìm x :

x : \(\dfrac{1}{2}+\) x : \(\dfrac{1}{4}\) + x : \(\dfrac{1}{8}\) +....+ x : \(\dfrac{1}{512}\) = 511

Answer 1

\(x:\dfrac{1}{2}+x:\dfrac{1}{4}+x:\dfrac{1}{8}+...+x:\dfrac{1}{512}=511\)

\(\Rightarrow x\left(2+4+8+...+512\right)=511\)

\(\Rightarrow\dfrac{\left(512+2\right).255}{2}.x=511\)

\(\Rightarrow65535x=511\)

\(\Rightarrow x=\dfrac{511}{65535}\)

Vậy.................

Answer 2

\(x:\dfrac{1}{2}+x:\dfrac{1}{4}+x:\dfrac{1}{8}+...+x:\dfrac{1}{512}=511\)

\(\Rightarrow x.\left(2+4+8+...+512\right)=511\)

\(\Rightarrow\dfrac{\left(512+2\right).255}{2}.x=511\)

\(\Rightarrow65535x=511\)

\(\Rightarrow x=\dfrac{511}{65535}\)

Vậy \(x=\dfrac{511}{65535}\)