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Gọi d=ƯC(2n+7;5n+17)
\(\Rightarrow\left\{{}\begin{matrix}2n+7⋮d\\5n+17⋮d\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}10n+35⋮d\\10n+34⋮d\end{matrix}\right.\)
\(\Rightarrow1⋮d\Rightarrow d=1\)
\(\Rightarrow\) phân số \(\dfrac{2n+7}{5n+17}\) tối giản
\(2A=\dfrac{4}{1.5}+\dfrac{6}{5.11}+\dfrac{8}{11.19}+\dfrac{10}{19.29}+\dfrac{12}{29.41}\)
\(2A=1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{19}+\dfrac{1}{19}-\dfrac{1}{29}+\dfrac{1}{29}-\dfrac{1}{41}\)
\(2A=1-\dfrac{1}{41}=\dfrac{40}{41}\)
\(A=\dfrac{40}{41}:2=\dfrac{20}{41}\)
\(3B=\dfrac{3}{1.4}+\dfrac{6}{4.10}+\dfrac{9}{10.19}+\dfrac{12}{19.31}\)
\(3B=1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{19}+\dfrac{1}{19}-\dfrac{1}{31}\)
\(3B=1-\dfrac{1}{31}=\dfrac{30}{31}\)
\(B=\dfrac{30}{31}:3=\dfrac{10}{31}\)
