Question

1/2-1/4-1/8-1/16-...-1/2024

Answer 1

=-1-(1/2+1/2^2+1/2^3+.....+1/2^10)

đặt A=(1/2+1/2^2+1/2^3+.....+1/2^10)

2A=2(1/2+1/2^2+1/2^3+.....+1/2^10)=1+1/2+...+1/2^9

A=(1+1/2+...+1/2^9)-(1/2+...+1/2^10)

A=1-1/2^10

=-1-1-1/2^10=......tự làm nha

Answer 2

Đề chắc sai e ạ, a sửa luôn :

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

\(A=\frac{1}{2}-\frac{1}{2^2}-...-\frac{1}{2^{10}}\)

\(2A=1-\frac{1}{2}-...-\frac{1}{2^9}\)

\(2A-A=\left(1-\frac{1}{2}-...-\frac{1}{2^9}\right)-\left(\frac{1}{2}-\frac{1}{2^2}-...-\frac{1}{2^{10}}\right)\)

\(A=1-\frac{1}{2}-...-\frac{1}{2^9}-\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{10}}\)

\(A=1-\left(\frac{1}{2}+\frac{1}{2}\right)+\frac{1}{2^{10}}\)

\(A=\frac{1}{2^{10}}\)

Answer 3

ok thank