\(D=\dfrac{5}{4.7}+\dfrac{5}{7.10}+\dfrac{5}{10.13}+...+\dfrac{5}{25.28}\)
\(=\dfrac{5}{3}\left(\dfrac{1}{4}-\dfrac{1}{28}\right)=\dfrac{5}{3}.\dfrac{6}{28}=\dfrac{5}{14}\)
\(E=\dfrac{2}{2.3}+\dfrac{2}{3.4}+\dfrac{2}{4.5}+...+\dfrac{2}{24.25}=2\left(\dfrac{1}{2}-\dfrac{1}{25}\right)=\dfrac{2.23}{50}=\dfrac{23}{25}.\)
\(\dfrac{D}{E}=\dfrac{5}{24}.\dfrac{25}{23}=\dfrac{125}{552}.\)
1. Tìm tỉ số \(\dfrac{x}{y}\) biết \(\dfrac{2x-y}{x+y}\)=\(\dfrac{2}{3}\)
2. Tìm x:
a) 3,8 : (2x) = \(\dfrac{1}{4}:2\dfrac{2}{3}\)
b) \(1\dfrac{1}{3}\) : 0,8 = \(\dfrac{2}{3}\) : (0,1x)
c) \(\dfrac{x}{-15}\) = \(\dfrac{-60}{x}\)
d) \(\dfrac{-2}{x}=\dfrac{-x}{\dfrac{8}{25}}\)
e) 0,2 : \(1\dfrac{1}{5}\)= \(\dfrac{2}{3}\) : (6x+7)
3. Tính A = \(\dfrac{8^{10}+4^{10}}{8^4+4^{11}}\)
a, D = \(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}\)
b, E = \(\dfrac{1}{1+2}+\dfrac{1}{1+2+3}+\dfrac{1}{1+2+3+4}+.......+\dfrac{1}{1+2+3+.......+9}\)
b) -x - 2 = \(\dfrac{5}{4}\) c) \(\dfrac{4}{3}-\left(x-\dfrac{1}{5}\right)=\left|\dfrac{-3}{10}+\dfrac{1}{2}\right|-\dfrac{1}{6}\) d) \(\dfrac{1}{3}-\left(\dfrac{2}{3}-x+\dfrac{5}{4}\right)=\dfrac{7}{12}-\left(\dfrac{5}{2}-\dfrac{13}{6}\right)\)
Tìm x, biết:
a) \(\left(5x+1\right)^2=\dfrac{36}{49}\)
b) \(\left[\left(-0,5\right)^3\right]^x=\dfrac{1}{64}\)
c) \(2020^{\left(x-2\right).\left(2x+3\right)}=1\)
d) \(\left(x+1\right)^{x+10}=\left(x+1\right)^{x+4}\) với \(x\in Z\)
e) \(\dfrac{3}{4}\sqrt{x}-\dfrac{1}{2}=\dfrac{1}{3}\)
1) So sánh các lũy thừa
a)\(4444^{3333}\) và \(3333^{4444}\)
b)\(348^4\) và \(4^{363}\)
c)\(1990^{10}+1999^9\) và \(1991^{10}\)
d)\(2^{2004}\) và \(5^{891}\)
e)\(10^{31}\) và \(2^{100}\)
2) Tìm x
\(\left(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{2014}\right).x=\dfrac{2013}{1}+\dfrac{2012}{2}+...+\dfrac{2}{2012}+\dfrac{1}{2013}\)
3) Tìm x,y thuộc Z để cho x-y+2xy=3
tìm x :
a) \(\dfrac{x+1}{7}+\dfrac{x+1}{8}=\dfrac{x+1}{9}+\dfrac{x+1}{10}\)
b) \(\dfrac{x+1}{12}+\dfrac{x^2}{11}=\dfrac{x+3}{10}+\dfrac{x+4}{9}\)
c) \(\dfrac{x-2}{x-1}=\dfrac{x+4}{x+7}\)
d)\(\dfrac{3x+2}{5x+7}=\dfrac{3x-1}{5x-3}\)
2 tìm x,y,z
a) \(\dfrac{x}{2}=\dfrac{y}{3},\dfrac{y}{4}=\dfrac{z}{5}vàx^2-y^2=-16\)
b)2x=3y,5x=7z và 3x-7y+5z=30
1. Tìm x biết :
a) \(\dfrac{x+4}{2001}+\dfrac{x+3}{2002}=\dfrac{x+2}{2003}+\dfrac{x+1}{2004}\)
b)\(\dfrac{x+2016}{11}+\dfrac{x+2017}{12}=\dfrac{x+2010}{5}\dfrac{x+2015}{10}\)
c)\(\dfrac{x+3}{5}+\dfrac{x+4}{4}+\dfrac{x+5}{3}+\dfrac{x+12}{2}=-1\)
d) (x-7)(x-6)=0
e)\(^{x^{ }2=4x}\)
f) (x-8)(x+2) đạt giá trị âm
g) \(\dfrac{x-2}{x-4}đạtgiatridương\)
Tính giá trị của các biểu thức sau:
a) A = \(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{299.300}\)
b) B = \(\dfrac{10^2}{16.26}+\dfrac{10^2}{26.36}+\dfrac{10^2}{36.46}+...+\dfrac{10^2}{86.96}\)
Tính tổng sau:
\(\dfrac{1}{2}+\dfrac{2}{4}+\dfrac{3}{8}+\dfrac{4}{16}+...+\dfrac{10}{2^{10}}\)
