Question

Tính: -1-1/2-1/4-1/8-...-1/1024

Answer 1

Đặt \(A=1+\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{1024}\)

\(\Rightarrow2A=2+1+\dfrac{1}{2}+...+\dfrac{1}{512}\)

\(\Rightarrow2A-A=\left(2+1+\dfrac{1}{2}+...+\dfrac{1}{512}\right)-\left(1+\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{1024}\right)\)

\(\Rightarrow A=2-\dfrac{1}{1024}\)

Từ đó: \(-1-\dfrac{1}{2}-\dfrac{1}{4}-...-\dfrac{1}{1024}\)

\(=-\left(1+\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{1024}\right)\)

\(=-\left(2-\dfrac{1}{1024}\right)\)

\(=\dfrac{1}{1024}-2\)

Vậy...