\(\Rightarrow A=\frac{3}{2}.\left(\frac{2}{5.7}+\frac{2}{7.9}+....+\frac{2}{59.61}\right)\)
\(\Rightarrow A=\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+......+\frac{1}{59}-\frac{1}{61}\right)\)
\(\Rightarrow A=\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{61}\right)\)
\(\Rightarrow A=\frac{3}{2}.\frac{56}{305}\)
\(\Rightarrow A=\frac{84}{305}\)
\(a\frac{3}{5}-\left(-\frac{1}{2}\right)+\frac{2}{5} b\frac{3}{7}.19\frac{1}{3}-\frac{3}{7}.33\frac{1}{3}c\left(\frac{3^4}{5}\right).\left(\frac{5^3}{3}\right)d\frac{11}{23}-\frac{5}{41}+\frac{13}{24}+0,5-\frac{36}{41}\)
\(A=3+\frac{3}{1+2}+\frac{3}{1+2+3}+.....+\frac{3}{1+2+3+4+...+100}\)
tính A
chứng minh
a , \(sinasin\left(\frac{\pi}{3}-a\right)sin\left(\frac{\pi}{3}+a\right)=\frac{1}{4}sin3a\) Áp dụng tính \(sin\frac{\pi}{9}sin\frac{2\pi}{9}sin\frac{4\pi}{9}\)
b , \(cosacos\left(\frac{\pi}{3}-a\right)cos\left(\frac{\pi}{3}+a\right)=\frac{1}{4}cos3a\) Áp dụng tính \(cos\frac{\pi}{18}cos\frac{5\pi}{18}cos\frac{7\pi}{18}\)
Tính:
\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{2009+2011}\)
\(\frac{a^3+b^3}{2}\ge\left(\frac{a+b}{2}\right)^{^{ }3}\)
\(\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\ge\frac{3}{2}\) với a,b,c>0
Bài 1 : Tìm x biết
a) \(13\frac{1}{3}\div1\frac{1}{3}=26\div\left(2x-1\right)\)
b) \(0,2:1\frac{1}{5}=\frac{2}{3}\div\left(6x+7\right)\)
c) \(\frac{37-x}{x+13}=\frac{3}{7}\)
d) \(\frac{x-1}{x+5}=\frac{6}{7}\)
e) \(2\frac{2}{\frac{3}{0,002}=}\frac{1\frac{1}{9}}{x}\)
Bài 2 : Tìm x,y,z biết:
a) \(\frac{x}{7}=\frac{4}{13}\)và x + y = 40
b) 3x = 2y , 7y = 57 và x - y + z = 32
c) \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{7-4}{4}\)và 2x + 3y - z = 50
Bài 3 .
a) 6,88 : x =12:27
b) \(8\frac{1}{3}\div11\frac{2}{3}=13:\left(2x\right)\)
Giải giúp mk
Mk đng cần gấp
Cho a, b, c. CMR:
\(\sqrt[3]{\left(\frac{2a}{b+c}\right)^2}+\sqrt[3]{\left(\frac{2b}{c+a}\right)^2}+\sqrt[3]{\left(\frac{2c}{a+b}\right)^2}\ge3\)
Xác định tập hợp bằng cách nêu tính chất:
a) A= {0,3,9,27,81}
b) B={-3,-2,-1,0,1,2,3,4}
c) C={2,4,9,16,25,36}
d) D={\(\frac{1}{3},\frac{2}{5},\frac{3}{7},\frac{4}{9}\)}