Question

Rút gọn biểu thức:A=1+1/2+1/2²+1/2³+...+1/2²⁰¹²

Answer 1

Ta có : 

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

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

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

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

\(A=\frac{2^{2013}-1}{2^{2012}}\)

Vậy \(A=\frac{2^{2013}-1}{2^{2012}}\)