Question

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

Answer 1

=>2A = 2+1+1/2+1/2²+...+1/2²⁰¹¹

=> 2A-A = (2+1+1/2+1/2²+...+1/2²⁰¹¹)-(1+1/2+...+1/2²⁰¹²) = 2-1/2²⁰¹²

 

Answer 2

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

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