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Đặt A = \(\dfrac{1}{3}+\dfrac{1}{15}+\dfrac{1}{35}+\dfrac{1}{63}+\dfrac{1}{99}+\dfrac{1}{143}+\dfrac{1}{195}\)
\(=\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+\dfrac{1}{7.9}+\dfrac{1}{9.11}+\dfrac{1}{11.13}+\dfrac{1}{13.15}\)
\(\Rightarrow2A=\)\(=\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+\dfrac{2}{9.11}+\dfrac{2}{11.13}+\dfrac{2}{13.15}\)
\(\Rightarrow2A=\) \(\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{13}-\dfrac{1}{15}\)
\(\Rightarrow2A=\) \(\dfrac{1}{1}-\dfrac{1}{15}=\dfrac{14}{15}\)
\(\Rightarrow A=\dfrac{14}{15}:2=\dfrac{7}{15}\)
Câu 14)
\(a,\\ =-\dfrac{3}{8}+\dfrac{8}{17}+\dfrac{-5}{8}-\dfrac{3}{5}+\dfrac{9}{17}\\ =\left(\dfrac{-3}{8}+\dfrac{-5}{8}\right)+\left(\dfrac{8}{17}+\dfrac{9}{17}\right)-\dfrac{3}{5}\\ =\left(-1\right)+1-\dfrac{3}{5}=0-\dfrac{3}{5}=\dfrac{-3}{5}\\ b,\\ =\dfrac{7}{15}.\dfrac{-15}{14}+\left(\dfrac{27}{16}-\dfrac{1}{8}\right):\dfrac{5}{8}\)
\(=\dfrac{-1}{2}+\dfrac{25}{16}.\dfrac{8}{5}=\dfrac{-1}{2}+\dfrac{5}{2}=2\\ c,\\ =\dfrac{2}{2}-\dfrac{2}{3}+\dfrac{2}{3}-\dfrac{2}{4}+.....+\dfrac{2}{99}-\dfrac{2}{100}\\ =1-\dfrac{1}{50}=\dfrac{49}{50}\)
Câu 15
\(a,2x+\dfrac{-1}{4}=\dfrac{3}{2}\\ 2x=\dfrac{3}{2}-\dfrac{-1}{4}=\dfrac{7}{4}\\ x=\dfrac{7}{4}:2=\dfrac{7}{8}\\ b,\dfrac{15}{x}=\dfrac{-3}{4}\\ x=\dfrac{15.4}{-3}=-20\)
mọi người ơi, đây có phải là đáp án đúng của bài 1 không ạ, nếu đúng thì giúp em viết ra giống như trên với ạ, em nhìn được nhưng 1 số chỗ không rõ lắm, huhu
Bài 34:
\(a,9.\left(x+28\right)=0\Rightarrow x+28=0\Rightarrow x=-28\\ b,\left(27-x\right)\left(x+9\right)=0\Rightarrow\left\{{}\begin{matrix}27-x=0\\x+9=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=27\\x=-9\end{matrix}\right.\\ c,\left(-x\right)\left(x-43\right)=0\Rightarrow\left\{{}\begin{matrix}-x=0\\x-43=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=0\\x=43\end{matrix}\right.\)
Bài 33
a) (62\(-\)81) \(-\)(12\(-\)59\(+\)9)
= 62\(-\)81\(-\)12\(+\)59\(-\)9
= (62\(-\)12)\(+\)(59\(-\)9)\(-\)81
= 50\(+\)50\(-\)81
= 100\(-\)81
= 19
b) (\(-\)75)\(+\)329\(+\)(\(-\)25)
= [(\(-\)75)\(+\)(\(-\)25)]\(+\)329
= \(-\)100\(+\)329
= 229
c) 32\(-\)34\(+\)36\(-\)38\(+\)40\(-\)42
= (32\(-\)42)\(+\)(\(-\)38\(+\)40)\(+\)(36\(+\)34)
= \(-\)10\(+\)2\(+\)70
= (70\(-\)10)\(+\)2
= 60\(+\)2
= 62
d) 92\(-\)(55\(-\)8)\(+\)(\(-\)45)
= 92\(-\)55\(+\)8\(+\)(\(-\)45)
= (92\(+\)8)\(+\)[(\(-\)55)\(+\)(\(-45\))]
= 100\(+\)(\(-\)100)
= 0