Question

Bài 2: Tính nhanh

1/2+1/4+1/8+...............+1/128

Lưu ý: Dấu / nghĩa là dấu gạch ngang phân số

 

Answer 1

Đặt \(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{128}\)

\(2A=1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{64}\)

\(2A-A=\left(1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{64}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{128}\right)\)

\(A=1-\frac{1}{128}=\frac{127}{128}\)

Ủng hộ mk nha ^_-

Answer 2

\(2\cdot A=1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{64}\)

\(A=\left(1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{64}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{128}\right)\)

\(A=1-\frac{1}{128}=\frac{128}{128}-\frac{1}{128}=\frac{127}{128}\)