Question

rút gọn biểu thức

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

Answer 1

2A = 2 + 1 + 1/2 + 1/2² + 1/2³ + ... + 1/2²⁰¹¹

mà A = 1 + 1/2 + 1/2² + 1/2³ + ... + 1/2²⁰¹²

2A - A = 2 - 1/2²⁰¹²

A = 2 - 1/2²⁰¹²

Answer 2

Ta có A=1+1/2+1/2^2+1/2^3+........+1/2^2012

=>2A=2+1+1/2+1/2^2+.......+1/2^2011

=>2A-A=(2+1+1/2+1/2^2+.....+1/2^2011)-(1+1/2+1+1/2^2+1/2^3+.....+1/2^2012)

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

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