Tìm x biết
4/1.5 + 4/5.9+... +4/97.101 = 2x+5/101
Tìm x biết
a) \(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{47.49}=\frac{24}{x+1}\)
b) \(\frac{4}{1.5}+\frac{4}{5.9}+\frac{4}{9.13}+...+\frac{4}{97.101}=\frac{2x+4}{101}\)
c) \(\frac{x-1}{2017}+\frac{x-2}{2016}=\frac{x-3}{2015}+\frac{x-4}{2014}\)
d) \(\frac{x+1}{2017}+\frac{x+2}{2016}=\frac{x+3}{2015}+\frac{x+4}{2014}\)
\(b)\) \(\frac{4}{1.5}+\frac{4}{5.9}+\frac{4}{9.13}+...+\frac{4}{97.101}=\frac{2x+4}{101}\)
\(\Leftrightarrow\)\(\frac{1}{1}-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{97}-\frac{1}{101}=\frac{2x+4}{101}\)
\(\Leftrightarrow\)\(1-\frac{1}{101}=\frac{2x+4}{101}\)
\(\Leftrightarrow\)\(\frac{100}{101}=\frac{2x+4}{101}\)
\(\Leftrightarrow\)\(100=2x+4\)
\(\Leftrightarrow\)\(2x=96\)
\(\Leftrightarrow\)\(48\)
Vậy \(x=48\)
Chúc bạn học tốt ~
\(a)\) \(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{47.49}=\frac{24}{x+1}\)
\(\Leftrightarrow\)\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{47.49}=\frac{48}{x+1}\)
\(\Leftrightarrow\)\(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{47}-\frac{1}{49}=\frac{48}{x+1}\)
\(\Leftrightarrow\)\(1-\frac{1}{49}=\frac{48}{x+1}\)
\(\Leftrightarrow\)\(\frac{48}{49}=\frac{48}{x+1}\)
\(\Leftrightarrow\)\(49=x+1\)
\(\Leftrightarrow\)\(x=48\)
Vậy \(x=48\)
Chúc bạn học tốt ~
Tìm x thỏa mãn
a, \(\frac{1}{1.4}+\frac{1}{4.7}+...+\frac{1}{97.100}=|\frac{x}{3}|\)
b, \(\frac{4}{1.5}+\frac{4}{5.9}+...+\frac{4}{97.101}=|\frac{5x-4}{101}|\)
c,\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{100}\right)=|x-1\frac{99}{100}|\)
a, \(\frac{1}{1.4}\)+\(\frac{1}{4.7}\)+......+\(\frac{1}{97.100}\)= |\(\frac{x}{3}\)|
\(\Rightarrow\)\(\frac{1}{3}\) ( \(\frac{3}{1.4}\)+\(\frac{3}{4.7}\)+.......+\(\frac{3}{97.100}\))= |\(\frac{x}{3}\)|
\(\Rightarrow\)\(\frac{1}{3}\) ( 1 - \(\frac{1}{4}\)+ \(\frac{1}{4}\)-\(\frac{1}{7}\)+......+\(\frac{1}{97}\)-\(\frac{1}{100}\)) = |\(\frac{x}{3}\)|
\(\Rightarrow\)\(\frac{1}{3}\) ( 1-\(\frac{1}{100}\)) = |\(\frac{x}{3}\)|
\(\Rightarrow\)\(\frac{1}{3}\) . \(\frac{99}{100}\) = |\(\frac{x}{3}\)|
\(\Rightarrow\)\(\frac{33}{100}\) = |\(\frac{x}{3}\)|
\(\Rightarrow\)\(\frac{x}{3}\)= \(\orbr{\begin{cases}\frac{33}{100}\\\frac{-33}{100}\end{cases}}\)
Với \(\frac{x}{3}\) = \(\frac{33}{100}\)
\(\Rightarrow\)100x= 33.3
\(\Rightarrow\)100x=99
\(\Rightarrow\)x=\(\frac{99}{100}\)
Với \(\frac{x}{3}\)=\(\frac{-33}{100}\)
\(\Rightarrow\)100x=-33.3
\(\Rightarrow\)100x=-99
\(\Rightarrow\)x=\(\frac{-99}{100}\)
Vậy x=\(\orbr{\begin{cases}\frac{99}{100}\\\frac{-99}{100}\end{cases}}\)
b, \(\frac{4}{1.5}\)+ \(\frac{4}{5.9}\)+......+ \(\frac{4}{97.101}\)= |\(\frac{5x-4}{101}\)|
\(\Rightarrow\)1-\(\frac{1}{5}\)+\(\frac{1}{5}\)-\(\frac{1}{9}\)+......+\(\frac{1}{97}\)-\(\frac{1}{101}\)= |\(\frac{5x-4}{101}\)|
\(\Rightarrow\)1-\(\frac{1}{101}\)= |\(\frac{5x-4}{101}\)
\(\Rightarrow\) \(\frac{100}{101}\)= |\(\frac{5x-4}{101}\)|
\(\Rightarrow\)\(\frac{5x-4}{101}\) =\(\orbr{\begin{cases}\frac{100}{101}\\\frac{-100}{101}\end{cases}}\)
Với \(\frac{5x-4}{101}\) =\(\frac{100}{101}\)
\(\Rightarrow\)(5x-4).101=100.101
\(\Rightarrow\)505x-404=10100
\(\Rightarrow\)505x=10504
\(\Rightarrow\)x=\(\frac{104}{5}\)
Với \(\frac{5x-4}{101}\)=\(\frac{-100}{101}\)
\(\Rightarrow\)(5x-4). 101=-100.101
\(\Rightarrow\)505x-404=-10100
\(\Rightarrow\)505x=-9696
\(\Rightarrow\)x=\(\frac{-96}{5}\)
Vậy x=\(\orbr{\begin{cases}\frac{104}{5}\\\frac{-96}{5}\end{cases}}\)
Tìm x:
a)4/1.5+4/5.9+...+4/9.13+...97/101=2.x+4/101
b)1/5.8+1/8.11+....+1/x.(x+3)=101/1840
c)1+1/3+1/6+1/10+...+2/x.(x+1)=1 2015/2017
câu c 1 2015/2017 là hỗn số nhé
a,Tính M= \(-\dfrac{4}{1.5}-\dfrac{4}{5.9}-..........-\dfrac{4}{\left(n+4\right).n}\)
b, Tìm x biết:
-4x ( x-5)-2x(8-2x)=-3
\(M=-\left(\dfrac{4}{1.5}+\dfrac{4}{5.9}+...+\dfrac{4}{n\left(n+4\right)}\right)\\ =-\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{n}-\dfrac{1}{n+4}\right)\\ =-\left(1-\dfrac{1}{n+4}\right)\\ =-\left(\dfrac{n+3}{n+4}\right)\)
\(-4x\left(x-5\right)-2x\left(8-2x\right)=-3\\ \Rightarrow-4x^2+20x-16x+4x^2=-3\\ \Rightarrow4x=-3\\ \Rightarrow x=-\dfrac{3}{4}\)
a) \(M=-\dfrac{4}{1.5}-\dfrac{4}{5.9}-...-\dfrac{4}{\left(n-4\right)n}\)
⇔ \(M=-\left(\dfrac{4}{1.5}+\dfrac{4}{5.9}+...+\dfrac{4}{\left(n-4\right)n}\right)\)
⇔ \(M=-\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{n-4}-\dfrac{1}{n}\right)\)
⇔ \(M=-\left(1-\dfrac{1}{n}\right)\)
⇔ \(M=-\dfrac{n-1}{n}\)
b) - 4x(x - 5) - 2x(8 - 2x) = -3
⇔ -4x2 + 20x - 16x + 4x2 = -3
⇔ 4x = -3
⇔ x = \(-\dfrac{3}{4}\)
Tính :
1.5 + 5.9 + 9.13 + .................. + 97.101
Tính :
1.5 + 5.9 + 9.13 + ............. + 97.101
Tính:
1.5 + 5.9 + 9.13 + 13.17 + ................ + 97.101
1/1.5+1/5.9+1/9.13+...+1/97.101
\(\frac{1}{1.5}+\frac{1}{5.9}+\frac{1}{9.13}+...+\frac{1}{97.101}\)
\(=\frac{1}{4}\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{97}-\frac{1}{101}\right)\)
\(=\frac{1}{4}.\left(1-\frac{1}{101}\right)\)
\(=\frac{1}{4}.\frac{100}{101}\)
\(=\frac{25}{101}\)
8/1.5+8/5.9+8/9.15+...+8/97.101