B = 2¹⁰⁰ - 2⁹⁹ + 2⁹⁸ - 2⁹⁷ + ... + 2²

B = ( 2¹⁰⁰ + 2⁹⁸ + ... + 2² ) - ( 2⁹⁹ + 2⁹⁷ + ... + 2³ )

B = ( 2¹⁰⁰ + 2⁹⁹ + 2⁹⁸ + 2⁹⁷ + ... + 2³ + 2² ) - 2( 2⁹⁹ + 2⁹⁷ + ... + 2³ )

B = ( 2¹⁰⁰ + 2⁹⁹ + 2⁹⁸ + 2⁹⁷ + ... + 2³ + 2² ) - ( 2¹⁰⁰ + 2⁹⁸ + ... +

2⁴ )

B = 2⁹⁹ + 2⁹⁷ + ... + 2³ + 2²

2²B = 2¹⁰¹ + 2⁹⁹ + ... + 2⁵ + 2⁴

4B - B = ( 2¹⁰¹ + 2⁹⁹ + ... + 2⁵ + 2⁴ ) - (  2⁹⁹ + 2⁹⁷ + ... + 2³ + 2² )

3B = 2¹⁰¹ + 2⁴ - 2³ - 2²

3B = 2¹⁰¹ + 16 - 8 - 4

3B = 2¹⁰¹ + 4

B = \(\dfrac{2^{101}+4}{3}\)

goc xOt dau ra  ? 

S tran=5*4=20m2

S tuong=(5*3*2)+(4*3*2)+20=74-14(S cua)=60(m2)

Vay ............ la 60 m2

`x + 2/4 - 4/3 = 4x - 1/12 + 2/3`

`x + 1/2 - 4/3 = 4x - 1/12 + 2/3`

`x -5/6 = 4x +7/12`

`-3x= 5/6+7/12`

`-3x = 17/12`

`x = 17/12 :(-3)`

`x = -17/36`

giúp mình với

\(-\dfrac{\sqrt{25^2}}{13}-\dfrac{\sqrt{81}}{17}+\dfrac{12}{13}+\left(-\dfrac{25}{17}\right)\)

\(=-\dfrac{25}{13}-\dfrac{9}{17}+\dfrac{12}{13}-\dfrac{25}{17}\)

`=(-25/13 +12/13) + (-9/17 - 25/17)`

`= (-13)/13 + (-34)/17`

`=(-1) + (-2)`

`=-3`

a, 4.(-\(\dfrac{1}{2}\))³ - 2(-\(\dfrac{1}{2}\))² + 3.(-\(\dfrac{1}{2}\)) + 1

= -\(\dfrac{1}{2}\) - \(\dfrac{1}{2}\) - \(\dfrac{3}{2}\) + 1

= -1 - \(\dfrac{3}{2}\) + 1

= -3/2

S = \(\dfrac{4}{2.4}\) + \(\dfrac{4}{4.6}\) + \(\dfrac{4}{6.8}\) +......+ \(\dfrac{4}{2012.2014}\) + \(\dfrac{4}{2014.2016}\)

S = 2. ( \(\dfrac{2}{2.4}+\dfrac{2}{4.6}+\dfrac{2}{6.8}+.....+\dfrac{2}{2012.2014}+\dfrac{2}{2014.2016}\))

S = 2.( \(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}+.....+\dfrac{1}{2014}-\dfrac{1}{2016}\))

S = 2.(\(\dfrac{1}{2}-\dfrac{1}{2016}\))

S = 2. \(\dfrac{1007}{2016}\)

S = \(\dfrac{1007}{1008}\)

\(\dfrac{3}{2}-|x-\dfrac{3}{4}|=\sqrt{\dfrac{9}{16}}\)

 ⇔ \(\dfrac{3}{2}-|x-\dfrac{3}{4}|=\dfrac{3}{4}\)

⇔ \(|x-\dfrac{3}{4}|=-\dfrac{3}{4}\)

⇔ \(x-\dfrac{3}{4}=-\dfrac{3}{4}\) hoặc      \(x-\dfrac{3}{4}=\dfrac{3}{4}\)

⇔ \(x\)          \(=0\)            ⇔  \(x\)          \(=\dfrac{3}{2}\)

Vậy pt có nghiệm : \(x=0\) hoặc \(x=\dfrac{3}{2}\)