Question

RÚT GỌN BIỂU THỨC: 

A=1+1\2+1\2^2+1\2^3+...+1\2^2012

Answer 1

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

\(\frac{1}{2}A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{2013}}\)

\(\frac{1}{2}A-A=\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{2013}}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2012}}\right)\)

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

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