Question

Tính nhanh

1/33 x ( 33/12+33/2020+333333/303030+33333333/42424242)

Answer 1

Sửa đề:

\(\frac{1}{33}\times\left(\frac{33}{12}+\frac{3333}{2020}+\frac{333333}{303030}+\frac{33333333}{42424242}\right)\)

\(=\frac{1}{33}\times\frac{33}{12}+\frac{1}{33}\times\frac{3333}{2020}+\frac{1}{33}\times\frac{333333}{303030}+\frac{1}{33}\times\frac{33333333}{42424242}\)

\(=\frac{1}{12}+\frac{33\times101}{33\times101\times20}+\frac{33\times10101}{33\times10101\times30}+\frac{33\times1010101}{33\times1010101\times42}\)

\(=\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)

\(=\frac{1}{3x4}+\frac{1}{4x5}+\frac{1}{5x6}+\frac{1}{6x7}\)

\(=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)

\(=\frac{1}{3}-\frac{1}{7}\)

\(=\frac{4}{21}\)