Question

Tính: \(A=2^{2012}-2^{2011}-2^{2010}-...-2^1-2^0\)

Answer 1

Ta có: A = 2^{2012 -} 2²⁰¹¹ - 2²⁰¹⁰ - ... - 2¹ - 2⁰

=> 2A = 2²⁰¹³ - 2²⁰¹² - 2²⁰¹¹ - ... - 2² - 2

=> 2A + A = (2²⁰¹³ - 2²⁰¹² - 2²⁰¹¹ - ... - 2² - 2) + (2^{2012 -} 2²⁰¹¹ - 2²⁰¹⁰ - ... - 2¹ - 2⁰)

=> 3A = 2²⁰¹³ - 2⁰

=> 3A = 2²⁰¹³ - 1

=> A = \(\frac{2^{2013}-1}{3}\)

Answer 2

Ta có: A = 2 2012 - 2 2011 - 2 2010 - ... - 2 1 - 2 0

=> 2A = 2 2013 - 2 2012 - 2 2011 - ... - 2 2 - 2 => 2A + A = (2 2013 - 2 2012 - 2 2011 - ... - 2 2 - 2) + (2 2012 - 2 2011 - 2 2010 - ... - 2 1 - 2 0 ) 

Answer 3

\(A=2^{2012}-2^{2011}-2^{2010}-...-2^1-2^0\)

\(\Rightarrow2A=2^{2013}-2^{2012}-2^{2011}-...-2^2-2^1\)

\(\Rightarrow2A+A=\left(2^{2013}-...-2^1\right)+\left(2^{2012}-...-2^0\right)\)

\(\Rightarrow3A=2^{2013}-2^0\Rightarrow A=\frac{2^{2013}-2^0}{3}\)