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\(E=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)....\left(1-\frac{1}{2006}\right)\left(1-\frac{1}{2007}\right)\)
\(E=\frac{1}{2}.\frac{2}{3}....\frac{2005}{2006}.\frac{2006}{2007}\)
\(E=\frac{1.2.3.4...2005.2006}{2.3.4.5....2006.2007}\)
\(E=\frac{1}{2007}\)
\(x:\frac{8}{9}=1\frac{3}{7}\)
\(x:\frac{8}{9}=\frac{10}{7}\)
\(x=\frac{10}{7}.\frac{8}{9}\)
\(x=\frac{80}{63}\)
\(x-1\frac{1}{4}=2\frac{1}{8}\)
\(x-\frac{5}{4}=\frac{17}{8}\)
\(x=\frac{17}{8}+\frac{5}{4}\)
\(x=\frac{17}{8}+\frac{10}{8}\)
\(x=\frac{27}{8}\)
\(x:\frac{8}{9}=1\frac{3}{7}\)
\(x:\frac{8}{9}=\frac{10}{7}\)
\(x=\frac{10}{7}\times\frac{8}{9}\)
\(x=\frac{80}{63}\)
#Y/n
\(1\)\(\frac{1}{3}x1\)\(\frac{1}{4}x1\)\(\frac{1}{5}x...x1\)\(\frac{1}{8}\)
\(=\frac{4}{3}x\)\(\frac{5}{4}x\)\(\frac{6}{5}\)\(x...x\)\(\frac{9}{8}\)
Tự tính nốt
\(1\frac{1}{3}\times1\frac{1}{4}\times1\frac{1}{5}\times1\frac{1}{6}\times1\frac{1}{7}\times1\frac{1}{8}.\)
= \(\frac{4}{3}\times\frac{5}{4}\times\frac{6}{5}\times\frac{7}{6}\times\frac{8}{7}\times\frac{9}{8}\times\frac{10}{9}\)
= \(\frac{4\times5\times6\times7\times8\times9\times10}{3\times4\times5\times6\times7\times8\times9}\)
= \(\frac{10}{3}\)
\(1\frac{1}{3}\times1\frac{1}{4}\times1\frac{1}{5}\times...\times1\frac{1}{8}\)
\(=\frac{4}{3}\times\frac{5}{4}\times\frac{6}{5}\times...\times\frac{9}{8}\)
\(=\frac{9}{3}\)