\(\frac{1}{4x9}+\frac{1}{9x14}+\frac{1}{14x19}+\frac{1}{44x49}\)
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tớ nghĩ là A = B
nếu đúng thì tk hộ tớ với , tớ đang bị âm 998 điểm !
Sửa đề: \(G=\frac{3}{4\times9}+\frac{3}{9\times14}+\frac{3}{14\times19}+\cdots+\frac{3}{34\times39}\)
Ta có: \(G=\frac{3}{4\times9}+\frac{3}{9\times14}+\frac{3}{14\times19}+\cdots+\frac{3}{34\times39}\)
\(=\frac35\times\left(\frac{5}{4\times9}+\frac{5}{9\times14}+\cdots+\frac{5}{34\times39}\right)\)
\(=\frac35\times\left(\frac14-\frac19+\frac19-\frac{1}{14}+\cdots+\frac{1}{34}-\frac{1}{39}\right)\)
\(=\frac35\times\left(\frac14-\frac{1}{39}\right)=\frac35\times\frac{35}{156}=\frac{7}{52}\)
\(=\dfrac{1}{5}\left(\dfrac{5}{4\cdot9}+\dfrac{5}{9\cdot14}+...+\dfrac{5}{1999\cdot2004}\right)\)
\(=\dfrac{1}{5}\left(\dfrac{1}{4}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{14}+...+\dfrac{1}{1999}-\dfrac{1}{2004}\right)\)
\(=\dfrac{1}{5}\left(\dfrac{1}{4}-\dfrac{1}{2004}\right)=\dfrac{1}{5}\cdot\dfrac{125}{501}=\dfrac{25}{501}\)
$\textbf{A}$
$A=\dfrac{2^{12}\cdot3^5-4^6\cdot9^2}{(2^2\cdot3)^6+8^4\cdot3^5}-\dfrac{5^{10}\cdot7^3-25^5\cdot49^2}{(125\cdot7)^3+5^9\cdot14^3}$
$=\dfrac{2^{12}\cdot3^5-2^{12}\cdot3^4}{2^{12}\cdot3^6+2^{12}\cdot3^5}-\dfrac{5^{10}\cdot7^3-5^{10}\cdot7^4}{5^9\cdot7^3+2^3\cdot5^9\cdot7^3}$
$=\dfrac{2^{12}\cdot3^4(3-1)}{2^{12}\cdot3^5(3+1)}-\dfrac{5^{10}\cdot7^3(1-7)}{5^9\cdot7^3(1+8)}$
$=\dfrac{2}{12}-\dfrac{-30}{9}$
$=\dfrac16+\dfrac{10}{3}$
$=\boxed{\dfrac72}.$
$\textbf{B}$
$B=\dfrac{\left(-\dfrac12\right)^3-\left(\dfrac34\right)^3\cdot(-2)^2}{2\cdot(-1)^5+\left(\dfrac34\right)^2-\dfrac38}$
$=\dfrac{-\dfrac18-\dfrac{27}{64}\cdot4}{-2+\dfrac9{16}-\dfrac38}$
$=\dfrac{-\dfrac18-\dfrac{27}{16}}{-2+\dfrac3{16}}$
$=\dfrac{-\dfrac{29}{16}}{-\dfrac{29}{16}}$
$=\boxed{1}.$
\(A=\frac{2}{1.5}+\frac{2}{5.9}+\frac{2}{9.13}+....+\frac{2}{81.85}\)
\(\Rightarrow2A=\frac{4}{1.5}+\frac{4}{5.9}+\frac{4}{9.13}+....+\frac{4}{81.85}\)
\(\Rightarrow2A=1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+....+\frac{1}{81}-\frac{1}{85}\)
\(\Rightarrow2A=1-\frac{1}{85}\)
\(\Rightarrow A=\frac{84}{85}:2=\frac{42}{85}\)
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
Giup tui voi !!!!!!!!!!!!!!!!!!!!!!!!!!! Mai phai nop roi !!!!!!!!!!!!!!!!!!!
Đặt tổng trên là A
\(5A=\frac{5}{4x9}+\frac{5}{9x14}+\frac{5}{14x19}+...+\frac{5}{44x49}\)
\(5A=\frac{9-4}{4x9}+\frac{14-9}{9x14}+\frac{19-14}{14x19}+...+\frac{49-44}{44x49}\)
\(5A=\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+\frac{1}{14}-\frac{1}{19}+...+\frac{1}{44}-\frac{1}{49}\)
\(5A=\frac{1}{4}-\frac{1}{49}\Rightarrow A=\frac{49-4}{4x5x49}=\frac{45}{4x5x49}=\frac{9}{4x49}\)