Tính A = (3/2^2) * (8/3^2) * (15/4^2) *....* (899/30^2)
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Gọi biểu thức là A
A=\(\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}...\frac{899}{30^2}\)
A=\(\frac{3.8.15...899}{2^2.3^2.4^2...30^2}\)
A=\(\frac{3.8.15...899}{4.9.16...900}\)
A=\(\frac{3}{4}.\frac{8}{9}.\frac{15}{16}...\frac{899}{900}\)
a) \(x-\dfrac{3}{5}=\dfrac{4}{-10}\)
\(x=\dfrac{4}{-10}+\dfrac{3}{5}\)
\(x=\dfrac{-4}{10}+\dfrac{6}{10}\)
\(x=\dfrac{1}{5}\)
b) \(\dfrac{3}{x}-2=\dfrac{4}{x}+4\)
\(\dfrac{3}{x}-2+2=\dfrac{4}{x}+4+2\)
\(\dfrac{3}{x}=\dfrac{4}{x}+4\)
\(\dfrac{3}{x}=\dfrac{4x+4}{x}\)
\(3x=\left(4x+4\right)x\)
\(3x=5x\cdot x+4x\)
\(3x=x\left(5x+4\right)\)
\(3=5x+4\)
\(5x=-1\)
\(x=\dfrac{-1}{5}\)
\(a,\Leftrightarrow\left[{}\begin{matrix}-\dfrac{4}{3}x+\dfrac{1}{2}=\dfrac{1}{2}\\-\dfrac{4}{3}x+\dfrac{1}{2}=-\dfrac{1}{2}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{3}{4}\end{matrix}\right.\\ c,\Leftrightarrow\left(\dfrac{1}{2}\right)^x\left(1+\dfrac{1}{4}\right)=\dfrac{5}{4}\\ \Leftrightarrow\left(\dfrac{1}{2}\right)^x=1\Leftrightarrow x=0\)
b: Ta có: \(3^x+3^{x+2}=20\)
\(\Leftrightarrow3^x\cdot10=20\)
\(\Leftrightarrow3^x=2\left(loại\right)\)
a.\(\frac{1}{4}+\frac{1}{8}\)
b.\(\frac{1}{2}+\frac{1}{4}\)
A=\(\dfrac{3}{1}\).(\(\dfrac{3}{2.5}\)+\(\dfrac{3}{5.8}\)+...+\(\dfrac{3}{98.101}\))
A=3.(\(\dfrac{1}{2}\)-\(\dfrac{1}{5}\)+\(\dfrac{1}{5}\)-\(\dfrac{1}{8}\)+...+\(\dfrac{1}{98}\)-\(\dfrac{1}{101}\))
A=3.(\(\dfrac{1}{2}\)-\(\dfrac{1}{101}\))
A=3.\(\dfrac{98}{202}\)
A=\(\dfrac{294}{202}\)=\(\dfrac{147}{101}\)
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