Question

[Trần Thu An]

Rút gọn biểu thức: A 1+1/2+1/2²+1/2³+....+1/2²⁰¹⁹

        ^{Các bạn giúp mình với, gấp gấp}

Answer 1

[Đặng Anh Thư]

A=\(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\)\(\frac{1}{2^{2019}}\)

2A= \(2\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2019}}\right)\)

2A= \(2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2018}}\)

2A-A=\(\left(1+2+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2018}}\right)\)\(-\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2019}}\right)\)

A= \(2-\frac{1}{2^{2019}}\)

A=\(\frac{2^{2020}}{2^{2019}}-\frac{1}{2^{2019}}\)

A=\(\frac{2^{2020}-1}{2^{2019}}\)