Bài 1: Thực hiện phép tính 1 cách hợp lý;\(a\)) \(Cho\) B\(=\) \(\frac{\left(5-\frac{5}{13}+\frac{5}{19}-\frac{5}{27}\right).4024.4026}{\left(10-\frac{10}{13}+\frac{10}{19}-\frac{10}{27}\right).2012.2013}\) \(b\)) \(Cho\)\(A\)\(=\)\(\frac{11}{210}-\left(\frac{16}{15.31}+\frac{13}{31.44}+\frac{13}{22.70}\right)\) \(c\)) \(\frac{3}{200}-\frac{3}{110}-\frac{3}{90}-\frac{3}{72}-\frac{3}{56}-...-\frac{3}{2}\) ...
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Bài 1: Thực hiện phép tính 1 cách hợp lý;
\(a\)) \(Cho\) B\(=\) \(\frac{\left(5-\frac{5}{13}+\frac{5}{19}-\frac{5}{27}\right).4024.4026}{\left(10-\frac{10}{13}+\frac{10}{19}-\frac{10}{27}\right).2012.2013}\)
\(b\)) \(Cho\)\(A\)\(=\)\(\frac{11}{210}-\left(\frac{16}{15.31}+\frac{13}{31.44}+\frac{13}{22.70}\right)\)
\(c\)) \(\frac{3}{200}-\frac{3}{110}-\frac{3}{90}-\frac{3}{72}-\frac{3}{56}-...-\frac{3}{2}\)
\(d\)) \(Cho\)\(C=\)\(\frac{\frac{1}{29}+\frac{1}{11}-\frac{1}{2013}}{\frac{1}{29}+\frac{1}{11}-\frac{1}{2013}+\frac{1}{11}.\frac{1}{29}.\frac{1}{2013}}+\frac{1}{11.2013+29.2013-318}\)
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Câu a)
\(B=\frac{\left(5-\frac{5}{13}+\frac{5}{19}-\frac{5}{27}\right)\cdot4024\cdot4026}{\left(10-\frac{10}{13}+\frac{10}{19}-\frac{10}{27}\right)\cdot2012\cdot2013}\)
\(\Leftrightarrow B=\frac{\left(5\cdot1-5\cdot\frac{1}{13}+5\cdot\frac{1}{19}-5\cdot\frac{1}{27}\right)\cdot2012\cdot2\cdot2013\cdot2}{\left(10\cdot1-10\cdot\frac{1}{13}+10\cdot\frac{1}{19}-10\cdot\frac{1}{27}\right)\cdot2012\cdot2013}\)
\(\Leftrightarrow B=\frac{5\left(1-\frac{1}{13}+\frac{1}{19}-\frac{1}{27}\right)\cdot2\cdot2}{5\cdot2\left(1-\frac{1}{13}+\frac{1}{19}-\frac{1}{27}\right)}\)
\(\Leftrightarrow B=2\)