Question

D=1/2+1/2^2+1/2^3+...+1/2^9.Tính câu này hộ mình với

 

Answer 1

\(D=\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^9}\)
\(\Rightarrow2D=1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^8}\)
\(\Rightarrow2D-D=\left(1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^8}\right)-\left(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^9}\right)\)
\(\Rightarrow D=1-\dfrac{1}{2^9}\)