Question

Tính B :

\(B=512-\dfrac{512}{2}-\dfrac{512}{2^2}-\dfrac{512}{2^3}-...-\dfrac{512}{2^{10}}\)

Answer 1

\(B=512-\dfrac{512}{2}-\dfrac{512}{2^2}-....-\dfrac{512}{2^{10}}\)

\(=512-\left(\dfrac{512}{2}+\dfrac{512}{2^2}+....+\dfrac{512}{2^{10}}\right)\)

\(=512-\left[512\left(\dfrac{1}{2}+\dfrac{1}{2^2}+....+\dfrac{1}{2^{10}}\right)\right]\)

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

\(2A=1+\dfrac{1}{2}+...+\dfrac{1}{2^9}\)

\(\Rightarrow2A-A=1-\dfrac{1}{2^{10}}\)

\(\Rightarrow A=1-\dfrac{1}{2^{10}}\)

\(\Rightarrow B=512-\left(512.A\right)=512-\left[512.\left(1-\dfrac{1}{2^{10}}\right)\right]\)

\(=512-512.\dfrac{1023}{1024}=512-\dfrac{1023}{2}=\dfrac{1}{2}\)