\(S=2^{2009}-2^{2008}-2^{2007}-...-2^2-2-1\)

\(2S=2^{2010}-2^{2009}-2^{2008}-...-2^3-2^2-2\)

\(2S-S=2^{2010}-1\)

\(S=2^{2010}-1\)

Mọi người tk cho mình nha. Mình cảm ơn nhiều ^.< ( Cô bé tháng 1 )

S = 2²⁰⁰⁹ - 2²⁰⁰⁸ - 2²⁰⁰⁷ - ... - 2² - 2 - 1 => 2S = 2²⁰¹⁰ - 2²⁰⁰⁹ - 2²⁰⁰⁸ - ... - 2³ - 2² - 2

S = 2S - S = (2²⁰¹⁰ - 2²⁰⁰⁹ - 2²⁰⁰⁸ - ... - 2³ - 2² - 2) - (2²⁰⁰⁹ - 2²⁰⁰⁸ - 2²⁰⁰⁷ - ... - 2² - 2 - 1)

S = 2²⁰¹⁰ - 2²⁰⁰⁹ - 2²⁰⁰⁹ + 1 = 2²⁰¹⁰ - 2²⁰⁰⁹.2 + 1 = 2²⁰¹⁰ - 2²⁰¹⁰ + 1= 0 + 1 = 1

Tìm max của biểu thức: 1 3 4 2 + − x x .

a) \(\dfrac{2}{5}+\dfrac{4}{5}\times\dfrac{5}{2}\)

\(=\dfrac{2}{5}+\dfrac{4\times5}{5\times2}\)

\(=\dfrac{2}{5}+\dfrac{4}{2}\)

\(=\dfrac{2}{5}+2\)

\(=\dfrac{2}{5}+\dfrac{10}{5}\)

\(=\dfrac{12}{5}\)

b) \(\dfrac{2008}{2009}-\dfrac{2009}{2008}+\dfrac{1}{2009}+\dfrac{2007}{2008}\)

\(=\left(1-\dfrac{1}{2009}\right)-\left(1+\dfrac{1}{2008}\right)+\dfrac{1}{2009}+\left(1-\dfrac{1}{2008}\right)\)

\(=1-\dfrac{1}{2009}-1-\dfrac{1}{2008}+\dfrac{1}{2009}+1-\dfrac{1}{2008}\)

\(=\left(1-1+1\right)-\left(\dfrac{1}{2009}-\dfrac{1}{2009}\right)-\left(\dfrac{1}{2008}+\dfrac{1}{2008}\right)\)

\(=1-\dfrac{2}{2008}\)

\(=\dfrac{2008}{2008}-\dfrac{2}{2008}\)

\(=\dfrac{2006}{2008}\)

\(=\dfrac{1003}{1004}\)

a: =2/5+4/2

=2/5+2

=12/5

b: \(=1-\dfrac{1}{2009}-1-\dfrac{1}{2008}+\dfrac{1}{2009}+1-\dfrac{1}{2008}\)

\(=1-\dfrac{2}{2008}=1-\dfrac{1}{1004}=\dfrac{1003}{1004}\)