​Bằng miệng

B = \(\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{19}}\)

=> 3B = \(\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^{18}}\)

=> 3B - B = \(\dfrac{1}{3}-\dfrac{1}{3^{19}}\)

=> 2B = \(\dfrac{1}{3}-\dfrac{1}{3^{19}}\)

=> B = \(\dfrac{\dfrac{1}{3}-\dfrac{1}{3^{19}}}{2}\)
@Hà Cao Thu

d, (12\(\dfrac{7}{8}-10\dfrac{13}{8}\)) : x - 1\(\dfrac{7}{33}:\dfrac{8}{11}=1\dfrac{2}{3}\)

<=> \(\dfrac{5}{4}:x-\dfrac{5}{3}=\dfrac{5}{3}\)

<=> \(\dfrac{5}{4}:x=\dfrac{10}{3}\)

<=> x = \(\dfrac{3}{8}\)
@Nguyễn Gia Hân

c, \(\dfrac{2}{3}\left(-3x-\dfrac{6}{5}\right)-\dfrac{5}{7}\left(\dfrac{49}{15}-14x\right)=-2\dfrac{1}{3}\)

<=> (-2x - \(\dfrac{4}{5}\)) - (\(\dfrac{7}{3}-10x\)) = -2\(\dfrac{1}{3}\)

<=> -2x - \(\dfrac{4}{5}-\dfrac{7}{3}+10x=-2\dfrac{1}{3}\)

<=> 8x - \(\dfrac{47}{15}=-\dfrac{64}{3}\)

<=> 8x = \(-\dfrac{91}{5}\)
<=> x = \(-\dfrac{91}{40}\)
@Nguyễn Gia Hân

b, \(\dfrac{3}{4}\left(x-\dfrac{8}{9}\right)-5\left(x-\dfrac{11}{15}\right)+\dfrac{1}{2}x=5\dfrac{1}{12}\)

<=> \(\left(\dfrac{3}{4}x-\dfrac{2}{3}\right)-\left(5x-\dfrac{11}{3}\right)+\dfrac{1}{2}x=5\dfrac{1}{12}\)

<=> \(\dfrac{3}{4}x-\dfrac{2}{3}-5x+\dfrac{11}{3}+\dfrac{1}{2}x=\dfrac{61}{12}\)

<=> \(-\dfrac{15}{4}x+3=\dfrac{61}{12}\)

<=> \(-\dfrac{15}{4}x=\dfrac{25}{12}\)

<=> x = \(-\dfrac{5}{9}\)
@Nguyễn Gia Hân

a, (\(\dfrac{2}{9}\)(6x - \(\dfrac{3}{4}\)) - 3(\(\dfrac{1}{4}x-\dfrac{1}{5}\)) = \(\dfrac{-8}{15}\)

<=> (\(\dfrac{4}{3}x-\dfrac{1}{6}\)) - (\(\dfrac{3}{4}x-\dfrac{3}{5}\)) = \(\dfrac{-8}{15}\)

<=> \(\dfrac{4}{3}x-\dfrac{1}{6}-\dfrac{3}{4}x+\dfrac{3}{5}=\dfrac{-8}{15}\)

<=> \(\dfrac{7}{12}x+\dfrac{13}{30}=\dfrac{-8}{15}\)

<=> \(\dfrac{7}{12}x=\dfrac{-8}{15}-\dfrac{13}{30}\)

<=> \(\dfrac{7}{12}x=-\dfrac{29}{30}\)

<=> x = \(-\dfrac{58}{35}\)
@Nguyễn Gia Hân

A = 2¹ + 2² + 2³ + 2⁴ +... + 2²³ + 2²⁴ + 2²⁵
=> 2A = 2² + 2³ + 2⁴ + ... + 2²⁴ + 2²⁵ + 2²⁶
=> 2A - A = 2²⁶ - 2
=> A = 2²⁶ - 2
@Nhok Cá Tính

\(\dfrac{6^3+3\times6^3+3^3}{13}\)

= \(\dfrac{216+648+27}{13}\)

= \(\dfrac{891}{13}\)
@Trịnh Thị Thảo Nhi

70%.x + 0,3.x + x : 2 = 20
<=> x(70% + 0,3) + x : 2 = 20
<=> x + x : 2 = 20
<=> x.(\(\dfrac{1}{2}+1\)) = 20
<=> x.\(\dfrac{3}{2}=20\)
<=> x = \(\dfrac{40}{3}\)
@Khánh Linh

(x + \(\dfrac{3}{5}\))² + 1\(\dfrac{16}{25}=9\%:4,5\%\)
<=> x² + (\(\dfrac{3}{5}\))² + 1\(\dfrac{16}{25}=2\)
<=> x² + \(\dfrac{9}{25}+\dfrac{41}{25}=2\)
<=> x² + 2 = 2
<=> x² = 0
<=> x = 0
@Khánh Linh