G=3/2.5+3/5.7+3/7.9+...+3/2015.2017
H=3/2.5+3/5.7+3/7.9+...+3/2015.2017
(3/3.6+3/3.9+...+3/30.33). x+2/5=7/8
(1/8+1/24+1/48+1/440). x=5/9
x:3/4+2,5=15%+16
khó wá giúp mình với huhu
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NT
2
QT
1
18 tháng 4 2018
Đặt \(A=\frac{3}{3.5}+\frac{3}{5.7}+...+\frac{3}{x\left(x+2\right)}\)(sửa đề)
\(\Rightarrow A=\frac{1}{2}.3.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+2}\right)\)
\(\Rightarrow A=\frac{3}{2}\left(\frac{1}{3}-\frac{1}{x+2}\right)\)
\(\Rightarrow A=\frac{1}{2}-\frac{3}{2x+4}\)
29 tháng 4 2021
1:
Ta có: \(D=\dfrac{3}{5\cdot7}+\dfrac{3}{7\cdot9}+\dfrac{3}{9\cdot11}+...+\dfrac{3}{53\cdot55}\)
\(=\dfrac{3}{2}\left(\dfrac{2}{5\cdot7}+\dfrac{2}{7\cdot9}+\dfrac{2}{9\cdot11}+...+\dfrac{2}{53\cdot55}\right)\)
\(=\dfrac{3}{2}\left(\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}+...+\dfrac{1}{53}-\dfrac{1}{55}\right)\)
\(=\dfrac{3}{2}\left(\dfrac{1}{5}-\dfrac{1}{55}\right)\)
\(=\dfrac{3}{2}\left(\dfrac{11}{55}-\dfrac{1}{55}\right)\)
\(=\dfrac{3}{2}\cdot\dfrac{2}{11}=\dfrac{3}{11}\)
29 tháng 4 2021
2) Để A là số nguyên dương thì
\(\left\{{}\begin{matrix}x+2⋮x-5\\x-5>0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x-5+7⋮x-5\\x>5\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}7⋮x-5\\x>5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x-5\inƯ\left(7\right)\\x>5\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x-5\in\left\{1;-1;7;-7\right\}\\x>5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\in\left\{6;4;12;-2\right\}\\x>5\end{matrix}\right.\)
\(\Leftrightarrow x\in\left\{6;12\right\}\)
27 tháng 4 2020
1)a, \(0,5x-\frac{2}{3}x=\frac{7}{12}\) b) \(x:4\frac{1}{3}=-\frac{2}{5}\)
\(x\left(0,5-\frac{2}{3}\right)=\frac{7}{12}\) \(x=-\frac{2}{5}.4\frac{1}{3}\)
\(-\frac{1}{6}x=\frac{7}{12}\) \(x=-\frac{26}{15}\)
\(x=\frac{-7}{2}\)
c) \(\left(\frac{3x}{7}+1\right):\left(-4\right)=-\frac{1}{28}\) d) \(x+30\%x=-1,3\)
\(\frac{3x}{7}+1=-\frac{1}{28}.\left(-4\right)\) \(x\left(1+30\%\right)=-1,3\)
\(\frac{3x}{7}+1=\frac{1}{7}\) \(1,3x=-1,3\)
\(\frac{3x}{7}=-\frac{6}{7}\) \(x=-1,3:1,3\)
\(x=-6.7:7:3\) \(x=-1\)
\(x=-2\)
Bài 2:
\(\frac{3}{5.7}+\frac{3}{7.9}+...+\frac{3}{2019.2021}=\frac{3}{2}\left(\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{2019.2021}\right)\)
\(=\frac{3}{2}\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{2019}-\frac{1}{2021}\right)\)
\(=\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{2021}\right)\)
\(=\frac{3}{2}.\frac{2016}{10105}\)
\(=\frac{3024}{10105}\)
NT
2
14 tháng 7 2021
a) Ta có: \(\dfrac{3}{5\cdot7}+\dfrac{3}{7\cdot9}+...+\dfrac{3}{59\cdot61}\)
\(=\dfrac{3}{2}\left(\dfrac{2}{5\cdot7}+\dfrac{2}{7\cdot9}+...+\dfrac{2}{59\cdot61}\right)\)
\(=\dfrac{3}{2}\left(\dfrac{1}{5}-\dfrac{1}{61}\right)\)
\(=\dfrac{3}{2}\cdot\dfrac{56}{305}=\dfrac{84}{305}\)
G=\(\frac{3}{2.5}+\frac{3}{5.7}+\frac{3}{7.9}+...+\frac{3}{2015.2017}\)
G=\(3.\left(\frac{1}{2.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{2015.2017}\right)\)
G=\(3.\left(\frac{1}{2}.\frac{1}{5}+\frac{1}{5}.\frac{1}{7}+\frac{1}{7}.\frac{1}{9}+...+\frac{1}{2013}.\frac{1}{2015}+\frac{1}{2015}.\frac{1}{2017}\right)\)
G=\(3.\left(\frac{1}{2}+\frac{1}{2017}\right)\)
G=1.5
Anh ko bik có đúng ko nữa lâu quá rồi. Em thông cảm nhé
nhớ 3 câu x khác nhau nhé