$\textbf{A}$

$A=\dfrac{2^{12}\cdot3^5-4^6\cdot9^2}{(2^2\cdot3)^6+8^4\cdot3^5}-\dfrac{5^{10}\cdot7^3-25^5\cdot49^2}{(125\cdot7)^3+5^9\cdot14^3}$

$=\dfrac{2^{12}\cdot3^5-2^{12}\cdot3^4}{2^{12}\cdot3^6+2^{12}\cdot3^5}-\dfrac{5^{10}\cdot7^3-5^{10}\cdot7^4}{5^9\cdot7^3+2^3\cdot5^9\cdot7^3}$

$=\dfrac{2^{12}\cdot3^4(3-1)}{2^{12}\cdot3^5(3+1)}-\dfrac{5^{10}\cdot7^3(1-7)}{5^9\cdot7^3(1+8)}$

$=\dfrac{2}{12}-\dfrac{-30}{9}$

$=\dfrac16+\dfrac{10}{3}$

$=\boxed{\dfrac72}.$

$\textbf{B}$

$B=\dfrac{\left(-\dfrac12\right)^3-\left(\dfrac34\right)^3\cdot(-2)^2}{2\cdot(-1)^5+\left(\dfrac34\right)^2-\dfrac38}$

$=\dfrac{-\dfrac18-\dfrac{27}{64}\cdot4}{-2+\dfrac9{16}-\dfrac38}$

$=\dfrac{-\dfrac18-\dfrac{27}{16}}{-2+\dfrac3{16}}$

$=\dfrac{-\dfrac{29}{16}}{-\dfrac{29}{16}}$

$=\boxed{1}.$

\(A=\frac{2}{1.5}+\frac{2}{5.9}+\frac{2}{9.13}+....+\frac{2}{81.85}\)

\(\Rightarrow2A=\frac{4}{1.5}+\frac{4}{5.9}+\frac{4}{9.13}+....+\frac{4}{81.85}\)

\(\Rightarrow2A=1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+....+\frac{1}{81}-\frac{1}{85}\)

\(\Rightarrow2A=1-\frac{1}{85}\)

\(\Rightarrow A=\frac{84}{85}:2=\frac{42}{85}\)

tính A còn lại tự tính nha

a) A = 2/1x5 + 2/5x9 + 2/9x13 +....+2/81x85

\(\frac{2}{1x5}+\frac{2}{5x9}+\frac{2}{9x13}+...+\frac{2}{81x85}\)

\(A=1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+...+\frac{1}{81}-\frac{1}{85}\)

\(A=1-\frac{1}{85}\)

\(\Rightarrow A=\frac{84}{85}\)

k nha

Đề bài?

Đúng jui đó bn Hạ Ninh !!!

help

làm hộ đi mà ngày mai à nhầm chiều nay mk phải đi học rồi

Sửa đề: \(G=\frac{3}{4\times9}+\frac{3}{9\times14}+\frac{3}{14\times19}+\cdots+\frac{3}{34\times39}\)

Ta có: \(G=\frac{3}{4\times9}+\frac{3}{9\times14}+\frac{3}{14\times19}+\cdots+\frac{3}{34\times39}\)

\(=\frac35\times\left(\frac{5}{4\times9}+\frac{5}{9\times14}+\cdots+\frac{5}{34\times39}\right)\)

\(=\frac35\times\left(\frac14-\frac19+\frac19-\frac{1}{14}+\cdots+\frac{1}{34}-\frac{1}{39}\right)\)

\(=\frac35\times\left(\frac14-\frac{1}{39}\right)=\frac35\times\frac{35}{156}=\frac{7}{52}\)

\(\frac{5}{4.9}+\frac{5}{9.14}+...+\frac{5}{54.59}=\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+...+\frac{1}{54}-\frac{1}{59}=\frac{1}{4}-\frac{1}{59}=\frac{55}{236}\)