\(\left(\frac{1}{17}-1\right)\left(\frac{2}{17}-1\right)\left(\frac{3}{17}-1\right)...\left(\frac{99}{17}-1\right)\)
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\(A=\frac{18.\frac{19}{2}.\frac{20}{3}....\frac{36}{19}}{20.\frac{21}{2}.\frac{22}{3}...\frac{36}{17}}=\frac{\frac{18.19.20...36}{1.2.3...17.18.19}}{\frac{20.21.22....36}{1.2.3...17}}=\frac{18.19.\left(20.21...36\right)}{\left(1.2.3...17\right).18.19}.\frac{1.2.3...17}{20.21.22....36}=1\)
\(\frac{\left(1+17\right).\left(1+\frac{17}{2}\right).\left(1+\frac{17}{3}\right)...\left(1+\frac{17}{19}\right)}{\left(1+19\right).\left(1+\frac{19}{2}\right).\left(1+\frac{19}{3}\right)...\left(1+\frac{19}{17}\right)}\)
\(=\frac{18.\frac{19}{2}.\frac{20}{3}...\frac{36}{19}}{20.\frac{21}{2}.\frac{22}{3}...\frac{36}{17}}=\frac{18.19.20...36}{1.2.3...19}:\frac{20.21.22...36}{1.2.3...17}\)
\(=\frac{18.19.20...36}{1.2.3...19}.\frac{1.2.3...17}{20.21.22....36}=\frac{1.2.3...17.18...36}{1.2.3...19.20...36}=1\)
\(M=\frac{18.\frac{19}{2}.\frac{20}{3}...\frac{36}{19}}{20.\frac{21}{2}.\frac{22}{3}...\frac{36}{17}}=\frac{\frac{18.19.20...36}{2.3...19}}{\frac{20.21.22...36}{2.3...17}}=\frac{\frac{18.19}{18.19}}{1}=\frac{1}{1}=1\)
???????????????????? chúc bạn giả bài này nhé chịu thôi
\(\left(\frac{1}{17}-1\right)\left(\frac{2}{17}-1\right)\left(\frac{3}{17}-1\right)....\left(\frac{99}{17}-1\right)\)
= \(\left(\frac{1}{17}-\frac{17}{17}\right)\left(\frac{2}{17}-\frac{17}{17}\right)\left(\frac{3}{17}-\frac{17}{17}\right).......\left(\frac{99}{17}-\frac{17}{17}\right)\)
= \(\left(\frac{-16}{17}\right)\left(\frac{-15}{17}\right)\left(\frac{-14}{17}\right).......\left(\frac{82}{17}\right)\)
= \(\frac{\left(-16\right).\left(-15\right).\left(-14\right)......82}{17}\)