Question

D = 1+ 1/2+1/4+1/8+1/16+...+1/2024

Answer 1

\(D=1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+...+\dfrac{1}{2048}\) (sửa đề)

\(\dfrac{1}{2}\cdot D=\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+...+\dfrac{1}{4096}\)

\(D-\dfrac{1}{2}D=1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+...+\dfrac{1}{2048}-\left(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+...+\dfrac{1}{4096}\right)\)

\(\dfrac{1}{2}D=1-\dfrac{1}{4096}\)

\(\dfrac{1}{2}D=\dfrac{4095}{4096}\)

\(\Rightarrow D=\dfrac{4095}{4096}:\dfrac{1}{2}=\dfrac{4095}{2048}\)

Vậy \(D=\dfrac{4095}{2048}\)