Tìm x : \(\frac{2}{42}+\frac{2}{56}+\frac{2}{72}+...+\frac{2}{x\cdot\left(x+1\right)}\) =\(\frac{2}{9}\) (x thuộc N*)
Tìm x : \(\frac{2}{42}+\frac{2}{56}+\frac{2}{72}+...+\frac{2}{x\cdot\left(x+1\right)}=\frac{2}{9}\) ( x thuộc N*)
2.[1/42+1/56+1/72+...+1/x.(x+1)]=2/9
1/6.7+1/7.8+1/8.9+....+1/x.(x+1)=1/9
1/6-1/7+1/7-1/8+1/8-1/9+.....+1/x-1/x+1=1/9
1/6-1/x+1=1/9
1:(x+1)=1/6-1/9
x+1=1:(1/18)
x+1=18
x=18-1
x=17
Vậy x=17
Chúc em học tốt
Ủng hộ anh nha^^
2/42 + 2/56 + 2/72 + ... + 2/x.(x+1) = 2/9
2.[1/42 + 1/56 + 1/72 + ... + 1/x.(x+1)] = 2/9
1/6.7 + 1/7.8 + 1/8.9 + ... + 1/x.(x+1) = 2/9 : 2
1/6 - 1/7 + 1/7 - 1/8 + 1/8 - 1/9 + ... + 1/x - 1/x+1 = 2/9 . 1/2
1/6 - 1/x+1 = 1/9
1/x+1 = 1/6 - 1/9
1/x+1 = 6/36 - 4/36
1/x+1 = 2/36 = 1/18
=> x+1=18
=> x=18-1
=> x=17
Vậy x=17
Đặt VT là A ta có:
\(A=2\left(\frac{1}{6.7}+\frac{1}{7.8}+...+\frac{1}{x\left(x+1\right)}\right)\)
\(=2\left(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{x}-\frac{1}{x+1}\right)\)
\(=2\left(\frac{1}{6}-\frac{1}{x+1}\right)\)
Thay A vào ta có:\(2\left(\frac{1}{6}-\frac{1}{x+1}\right)=\frac{2}{9}\)
\(\frac{1}{6}-\frac{1}{x+1}=\frac{1}{9}\)
\(\frac{1}{x+1}=\frac{1}{18}\)
\(\Rightarrow x+1=18\)
\(\Rightarrow x=17\)
a) Tính
\(A=\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot\left(1-\frac{1}{4}\right)\cdot\cdot\cdot\left(1-\frac{1}{2014}\right)\cdot\left(1-\frac{1}{2015}\right)\cdot\left(1-\frac{1}{2016}\right)\)
b) Tìm x:
\(\frac{x-2}{12}+\frac{x-2}{20}+\frac{x-2}{30}+\frac{x-2}{42}+\frac{x-2}{56}+\frac{x-2}{72}=\frac{16}{9}\)
b)
\(x-2.\left(\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}\right)=\frac{16}{9}\)
\(x-2\cdot\left(\frac{1}{3}-\frac{1}{9}\right)=\frac{16}{9}\)
\(x-2=\frac{16}{9}:\left(\frac{1}{3}-\frac{1}{9}\right)\)
\(x-2=8\)
=> x = 10
a)
\(A=\frac{1}{2}.\frac{2}{3}\cdot\frac{3}{4}\cdot\cdot\cdot\frac{2013}{2014}\cdot\frac{2014}{2015}\cdot\frac{2015}{2016}\)
\(A=\frac{1}{2016}\)
A = ( 1 - 1/2) . ( 1 - 1/3 ) . (1-1/4) ....(1-1/2015) . (1-1/2016)
A= 1/2 . 2/3 . 3/4...2014/2015 . 2015/2016
A = 1 . 2 . 3 . 4 ... 2014 . 2015/ 2 . 3 . 4 ... 2015 . 2016
A = 1/ 2016
Tìm x:
a) x - \(\frac{20}{11.13}-\frac{20}{13.15}-\frac{20}{15.17}-...-\frac{20}{53.55}=\frac{3}{11}\)
b) \(\frac{2}{42}+\frac{2}{56}+\frac{2}{72}+...+\frac{2}{x\left(x+1\right)}=\frac{2}{9}\left(x\in N\cdot\right)\)
\(x-\frac{20}{11.13}-\frac{20}{13.15}-\frac{20}{15.17}-...-\frac{20}{53.55}=\frac{3}{11}\)
\(x-10\left(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+...+\frac{2}{53.55}\right)=\frac{3}{11}\)
\(x-10\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{53}-\frac{1}{55}\right)=\frac{3}{11}\)
\(x-10.\frac{4}{55}=\frac{3}{11}\)
\(x=1\)
Tìm x biết :
\(\left(\frac{x-2}{12}\right)+\left(\frac{x-2}{20}\right)+\left(\frac{x-2}{30}\right)+\left(\frac{x-2}{42}\right)+\left(\frac{x-2}{56}\right)+\left(\frac{x-2}{72}\right)=\frac{16}{9}\)
giúp mk nha
\(\left(x-2\right):\left(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\right)=\frac{16}{9}\)
\(\left(x-2\right):\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\right)=\frac{16}{9}\)
\(\left(x-2\right):\frac{2}{9}=\frac{16}{9}\)
\(x-2=\frac{32}{91}\)
\(x=\frac{32}{91}+2\)
\(x=\frac{212}{91}\)
tìm x thuộc N:
\(\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+...+\frac{2}{x\cdot\left(x+1\right)}=\frac{2}{9}\)
Đặt \(A=\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+...+\frac{2}{x\left(x+1\right)}\)
=> \(A=\frac{2}{6.7}+\frac{2}{7.8}+\frac{2}{8.9}+...+\frac{2}{x\left(x+1\right)}\)
\(\frac{A}{2}=\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+...+\frac{1}{x}-\frac{1}{x+1}\)
=> \(\frac{A}{2}=\frac{1}{6}-\frac{1}{x+1}=\frac{x+1-6}{6\left(x+1\right)}=\frac{x-5}{6\left(x+1\right)}\) => \(A=\frac{x-5}{3\left(x+1\right)}=\frac{2}{9}\)
<=> 3(x-5)=2(x+1) <=> 3x-15=2x+2 <=> x=17
Đáp số: x=17
Tìm x biết :
a, ( 4x - 9 ) . ( 2,5 + \(\frac{-7}{3}\). x ) = 0
b, \(\frac{1}{x\cdot\left(x+1\right)}\cdot\frac{1}{\left(x+1\right)\cdot\left(x+2\right)}\cdot\frac{1}{\left(x+2\right)\cdot\left(x+3\right)}-\frac{1}{x}=\frac{1}{2015}\)
a)
( 4x - 9 ) ( 2,5 + (-7/3) . x ) = 0
\(\Rightarrow\orbr{\begin{cases}4x-9=0\\2,5+\frac{-7}{3}x=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{9}{4}\\x=\frac{15}{14}\end{cases}}\)
P/s: đợi xíu làm câu b
b) \(\frac{1}{x\left(x+1\right)}\cdot\frac{1}{\left(x+1\right)\left(x+2\right)}\cdot\frac{1}{\left(x+2\right)\left(x+3\right)}-\frac{1}{x}=\frac{1}{2015}\)
\(\frac{1}{x}-\frac{1}{x+1}+\frac{1}{x+1}-\frac{1}{x+2}+\frac{1}{x+2}-\frac{1}{x+3}-\frac{1}{x}=\frac{1}{2015}\)
\(\frac{-1}{x+3}=\frac{1}{2015}\)
\(\Leftrightarrow x+3=-2015\)
\(\Leftrightarrow x=-2018\)
Vậy,.........
A/ Ta có số nào nhân với 0 cx = 0
Vậy từ đó suy ra 2 trường hợp
TH1\(4x-9=0\)
\(=>x=\frac{9}{4}\)
TH2 \(2,5+-\frac{7}{3}x=0\)
\(=>x=\frac{15}{14}\)
Tìm x biết \(\frac{x-2}{12}+\frac{x-2}{20}+\frac{x-2}{30}+\frac{x-2}{42}+\frac{x-2}{56}+\frac{x-2}{72}=\frac{16}{9}\)
\(\frac{x-2}{12}+\frac{x-2}{20}+\frac{x-2}{30}+\frac{x-2}{42}+\frac{x-2}{56}+\frac{x-2}{72}=\frac{16}{9}\)
\(\left(x-2\right)\cdot\left(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\right)=\frac{16}{9}\)
\(\left(x-2\right)\cdot\left(\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}\right)=\frac{16}{9}\)
\(\left(x-2\right)\cdot\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\right)=\frac{16}{9}\)
\(\left(x-2\right)\cdot\left(\frac{1}{3}-\frac{1}{9}\right)=\frac{16}{9}\)
\(\left(x-2\right)\cdot\left(\frac{3}{9}-\frac{1}{9}\right)=\frac{16}{9}\)
\(\left(x-2\right)\cdot\frac{2}{9}=\frac{16}{9}\)
\(x-2=\frac{16}{9}:\frac{2}{9}\)
\(x-2=\frac{16}{9}\cdot\frac{9}{2}\)
\(x-2=8\)
\(x=8+2\)
\(x=10\)
Vậy \(x=10\)
\(\left(x-2\right)\left(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}\right)=\)\(=\frac{16}{9}\)
\(\left(x-2\right)\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}+\frac{1}{8}-\frac{1}{9}\right)=\frac{16}{9}\)
\(\left(x-2\right)\left(\frac{1}{3}-\frac{1}{9}\right)=\frac{16}{9}\)
\(\left(x-2\right)\left(\frac{2}{9}\right)=\frac{16}{9}\)
2(x-2)=16
x-2=8
x=10
Tìm x:
a) \(\frac{3}{\left(x+2\right)\cdot\left(x+5\right)}\)+\(\frac{5}{\left(x+5\right)\cdot\left(x+10\right)}\)+\(\frac{7}{\left(x+10\right)\cdot\left(x+17\right)}\)= \(\frac{x}{\left(x+2\right)\cdot\left(x+17\right)}\)
Với x không thuộc (-2;-5;-10;-17)
b) \(\frac{2}{\left(x-1\right)\cdot\left(x-3\right)}\)+\(\frac{5}{\left(x-3\right)\cdot\left(x-8\right)}\)+\(\frac{12}{\left(x-8\right)\cdot\left(x-20\right)}\)-\(\frac{1}{20}\)= \(\frac{-3}{4}\)
Với x không thuộc (1;3;8;20)
c)\(\frac{x+1}{2019}\)+\(\frac{x+2}{2018}\)= \(\frac{x-3}{2017}\)\(\frac{x-4}{2016}\)
Tìm x:
\(\frac{\left(13\frac{2}{9}-15\frac{2}{3}\right)\cdot\left(30^2-5^4\right)}{\left(18\frac{3}{7}-17\frac{1}{4}\right)\cdot\left(25-12\cdot5^2\right)}\cdot x=\frac{\frac{2}{11}+\frac{3}{13}+\frac{4}{15}+\frac{5}{17}}{4\frac{1}{11}+\frac{5}{13}+\frac{9}{15}+\frac{13}{17}}\)