Question

A=1+1/2+1/2²+1/2³+.....+1/2²⁰¹²

^{lam on giai ho toi nhe}

Answer 1

Đề là gì z??????????                                                 

Answer 2

2A \(=2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2011}}\)

     \(\Rightarrow2A-A=2-\frac{1}{2^{2012}}\Rightarrow A=2-\frac{1}{2^{2012}}\)

ĐÚNG NHÉ

Answer 3

A=\(1+\frac{1}{2}\)+\(\frac{1}{2^2}\)+\(\frac{1}{2^3}\)+...+\(\frac{1}{2^{2012}}\)

2A=2+1+\(\frac{1}{2}\)+\(\frac{1}{2^2}\)+\(\frac{1}{2^3}\)+...+\(\frac{1}{2^{2011}}\)

2A-A=\(\left(2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2011}}\right)\)- \(\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2012}}\right)\)

A= 2-\(\frac{1}{2^{2012}}\)

Vậy biểu thức \(1+\frac{1}{2}\)+\(\frac{1}{2^2}\)+\(\frac{1}{2^3}\)+...+\(\frac{1}{2^{2012}}\) rút gọn thành 2 - \(\frac{1}{2^{2012}}\)