Question

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

Answer 1

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

\(B=512-512\left(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+..+\dfrac{1}{2^{10}}\right)\)

Đặt: \(L=\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{10}}\)

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

\(2L-L=1-\dfrac{1}{2^{10}}\Leftrightarrow L=1-\dfrac{1}{2^{10}}\)

Thay Vào B

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