Question

[Ngô Ngọc]

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

Answer 1

[doremon]

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

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

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