Question

Tính A

A=1/2+1/2^2+1/2^3+...+1/2^10

Answer 1

\(A=\dfrac{1}{2}+\dfrac{1}{2}^2+\dfrac{1}{2}^3+...+\dfrac{1}{2}\)¹⁰

   \(= (\dfrac{1}{2}+\dfrac{1}{2}^9)+(\dfrac{1}{2}^2+\dfrac{1}{2}^8)+(\dfrac{1}{2}^3+\dfrac{1}{2}^7)+\dfrac{1}{2}\)¹⁰

    \(= \dfrac{257}{512}+\dfrac{65}{256}+\dfrac{17}{128}+\dfrac{1}{1024}\)

    \(=( \dfrac{514}{1024}+\dfrac{136}{1024})+(\dfrac{260}{1024}+\dfrac{1}{1024})\)

   \(=\dfrac{650}{1024}+\dfrac{261}{1024}\)

   \(=\dfrac{911}{1024}\)