Question

-1-1/2-1/4-1/8-...-1/1024

Giúp tôi với, bí lắm rồi huhu

Answer 1

Đặt \(A=-1-\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-....-\frac{1}{1024}\)

\(=-\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{1024}\right)\)

Đặt \(B=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+....+\frac{1}{1024}\)

=> \(B=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{10}}\)

=> \(2B=2+1+\frac{1}{2^2}+...+\frac{1}{2^9}\)

=> \(B=2B-B=2-\frac{1}{2^{10}}\)

=> \(A=-\left(2-\frac{1}{2^{10}}\right)=-\left(2-\frac{1}{1024}\right)=-\frac{2047}{1024}\)