Question

Rút gọn

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

Answer 1

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

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

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

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

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

Answer 2

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

\(2a=2+1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{2011}}\)

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

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

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

Answer 3

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

2A - A = (2+1+1/2+1/2³ +..........+1/2²⁰¹²)- (1+1/2+1/2²+1/2³+...........+1/2²⁰¹²⁾

A= 2-1/2²⁰¹²

A=2013 -1/2²⁰¹²

Answer 4

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