ta có : \(\dfrac{3}{2}\)A= \(\dfrac{3}{4}+\)\(\left(\dfrac{3}{2}\right)^2+\left(\dfrac{3}{2}\right)^3+\)\(...+\left(\dfrac{3}{2}\right)^{2013}\) (1)

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

Lấy (1) trừ đi (2) vế theo vế:

\(\dfrac{3}{2}A-A=\dfrac{3}{4}-\dfrac{1}{2}-\dfrac{3}{2}+\left(\dfrac{3}{2}\right)^{2013}\)

\(\dfrac{1}{2}A=\left(\dfrac{3}{2}\right)^{2013}-\dfrac{5}{4}\Rightarrow A=\dfrac{3^{2013}}{2^{2012}}-\dfrac{5}{2}\)

ta có : \(B=\left(\dfrac{3}{2}\right)^{2013}:2=\dfrac{3^{2013}}{2^{2013}}.\dfrac{1}{2}=\dfrac{3^{2013}}{2^{2014}}\)

Vậy \(A-B=\dfrac{3^{2013}}{2^{2014}}-\left(\dfrac{3^{2013}}{2^{2012}}-\dfrac{5}{2}\right)\)

x

\(\Leftrightarrow-5< x< -\dfrac{1037}{1260}\)

=>\(x\in\left\{-4;-3;-2;-1\right\}\)

\(=\left(\frac{1}{2}+\frac{1}{3}\right):\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{2}.1\right):2^3\)

\(=\frac{5}{6}:\frac{1}{6}+\frac{1}{2}:8\)

\(=5+\frac{1}{16}\)

\(=\frac{81}{16}\)

Đừng cãi nhau mà đẩy câu của mình xuống        

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

\(\frac{3}{2}A=\frac{3}{4}+\left(\frac{3}{2}\right)^2+\left(\frac{3}{2}\right)^3+\left(\frac{3}{2}\right)^4+...+\left(\frac{3}{2}\right)^{2013}\)(2)

Lấy (2) trừ (1) ta được:

\(\frac{1}{2}A=\frac{3}{4}+\left(\frac{3}{2}\right)^{2013}-\frac{1}{2}-\frac{3}{2}=\left(\frac{3}{2}\right)^{2013}-\frac{5}{4}\)

\(A=\frac{\left(\frac{3}{2}\right)^{2013}-\frac{5}{4}}{\frac{1}{2}}=\left(\frac{3}{2}\right)^{2013}.2-\frac{5}{4}.2=\left(\frac{3}{2}\right)^{2013}.2-\frac{5}{2}\)

\(\Rightarrow B-A=\left(\frac{3}{2}\right)^{2013}\cdot\frac{1}{2}-\left(\frac{3}{2}\right)^{2013}.2+\frac{5}{2}=-\left(\frac{3}{2}\right)^{2014}+\frac{5}{2}\)

kết quả là (3/2)^2014-1

đúng đó

a) \(25^3:5^2=5^6:5^2=5^4=625\)

b) \(\left(\frac{3}{7}\right)^{21}:\left(\frac{9}{49}\right)^6=\left(\frac{3}{7}\right)^{21}:\left(\frac{3}{7}\right)^{12}=\left(\frac{3}{7}\right)^9\)

c) \(3-\left(-\frac{6}{7}\right)^0+\left(\frac{1}{2}\right)^2:2=3-1+\frac{1}{8}=\frac{17}{8}\)

a) \(25^3:5^2=5^6:5^2=5^{6-2}=5^4\)

Bài 1: 

a: \(A=\dfrac{\left(85+\dfrac{7}{30}-83-\dfrac{5}{18}\right):\dfrac{8}{3}}{\dfrac{1}{25}}\)

\(=\left(2+\dfrac{7}{30}-\dfrac{5}{18}\right)\cdot\dfrac{3}{8}\cdot25\)

\(=\dfrac{180+21-25}{90}\cdot\dfrac{75}{8}\)

\(=\dfrac{176}{90}\cdot\dfrac{75}{8}=\dfrac{55}{3}\)

=>12,5% của A là 55/8x1/8=55/64

b: \(B=\dfrac{\left(6+\dfrac{3}{5}-3-\dfrac{3}{14}\right)\cdot\dfrac{36}{5}}{19.75:2.5}\)

\(=\dfrac{\left(3+\dfrac{27}{70}\right)\cdot\dfrac{36}{5}}{\dfrac{79}{10}}\)

\(=\dfrac{\dfrac{210+27}{70}\cdot\dfrac{36}{5}}{\dfrac{79}{10}}\)

\(=\dfrac{4266}{175}\cdot\dfrac{10}{79}=\dfrac{108}{35}\)

=>5% là 108/35x1/20=27/175

toán lớp 7

`#3107.101107`

`-3^2 + {-54 \div [-2^8 + 7] * (-2)^2}`

`= -9 + [-54 \div (-256 + 7) * 4]`

`= -9 + [-54 \div (-249) * 4]`

`= -9 + (18/83 * 4)`

`= -9 + 72/83`

`= -675/83`

______

`31 * (-18) + 31 * (-81) - 31`

`= 31 * (-18 - 81 - 1)`

`= 31 * (-100)`

`= -3100`

___

`(-12) * 47 + (-12) * 52 + (-12)`

`= (-12) * (47 + 52 + 1)`

`= (-12) * 100`

`= -1200`

___

`13 * (23 + 22) - 3 * (17 + 28)`

`= 13 * 45 - 3 * 45`

`= 45 * (13 - 3)`

`= 45 * 10`

`= 450`

____

`-48 + 48 * (-78) + 48 * (-21)`

`= 48 * (-1 - 78 - 21)`

`= 48 * (-100)`

`= -4800`

b, \(\left(\frac{3}{7}\right)^{21}:\left(\frac{9}{49}\right)^6=\left(\frac{3}{7}\right)^{21}:\left[\left(\frac{3}{7}\right)^2\right]^6=\left(\frac{3}{7}\right)^{21}:\left(\frac{3}{7}\right)^{12}=\left(\frac{3}{7}\right)^{21-12}=\left(\frac{3}{7}\right)^9\)