Question

Rút gọn biểu thức :A=1+\(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2012}}\)

Answer 1

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

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

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

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

Answer 2

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

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

=>  \(2A=2+1+...+\frac{2}{2^{2011}}\)

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

=> \(A=2-\frac{1}{2012}\)