B= (151515/161616+17^9/17^10)-(1500/1600-176/187)
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\(-7\left(x+9\right)-3\left(5-x\right)=2\\ \Rightarrow-7x-63-15+3x-2=0\\ \Rightarrow-4x-80=0\\ \Rightarrow-4x=80\\ \Rightarrow x=-20\)
-7x+(-63)-15+3x=2
[(-7x)+3x]+[(-63)-15]=2
-4x+(-78)=2
-4x=2+(-78)
-4x=-76
x=(-76)\(\div\)(-4)
x=19
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\(-7x-63-15+3x=2\Leftrightarrow-4x-78=2\Leftrightarrow x=-20\)
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\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{380}\)
\(=\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{19\cdot20}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{19}-\frac{1}{20}\)
\(=\frac{1}{2}-\frac{1}{20}=\frac{9}{20}\)
TL
\(\frac{1}{6}\)+\(\frac{1}{12}\)+\(\frac{1}{20}\)+....+\(\frac{1}{380}\)
=>\(\frac{1}{2.3}\)+\(\frac{1}{3.4}\)+\(\frac{1}{4.5}\)+...+\(\frac{1}{19.20}\)
=>\(\frac{1}{2}\)-\(\frac{1}{3}\)+\(\frac{1}{3}\)-\(\frac{1}{4}\)+\(\frac{1}{4}\)+....+\(\frac{1}{19}\)-\(\frac{1}{20}\)
=>\(\frac{1}{2}\)-\(\frac{1}{20}\)
=>\(\frac{9}{20}\)
HT
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Gọi ƯCLN(2n+1005;4n+2011)=d(\(d\in\)N*)
\(\Rightarrow2n+1005⋮d\Rightarrow4n+2010⋮d\Rightarrow4n+2011-4n-2010⋮d\Leftrightarrow1⋮d\Leftrightarrow d=1\)
Vậy ta có đpcm
gọi d là ƯC(2n+1005,4n+2011)(d\(\in\)N*)
theo bài ra ta có
2n+1005\(⋮\)d\(\Rightarrow\)2(2n+1005)\(⋮\)d\(\Rightarrow\)4n+2010\(⋮\)d
4n+2011\(⋮\)d
\(\Rightarrow\)(4n+2011)-(4n+2010)\(⋮\)d
\(\Rightarrow\)4n+2011-4n+2010\(⋮\)d
\(\Rightarrow\)1\(⋮\)d
\(\Rightarrow\)d=1
vậy với mọi n \(\in\)N thì \(\dfrac{2n+1005}{4n+2011}\) là phân số tối giản