Question

20/9.x=1/12+1/20+1/30+1/42+1/56+1/72

Answer 1

\(\frac{20}{9}x=\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\)

\(\frac{20}{9}x=\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}\)

\(\frac{20}{9}x=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-.....-\frac{1}{9}\)

\(\frac{20}{9}x=\frac{1}{3}-\frac{1}{9}=\frac{2}{9}\)

\(x=\frac{2}{9}:\frac{20}{9}=\frac{1}{10}\)

Answer 2

20/9 . x = 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72

20/9 . x = 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7 + 1/7.8 + 1/8.9

20/9 . x = 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/8 - 1/9

20/9 . x  = 1/3 - 1/9 = 2/9

x = 2/9 : 20/9 = 2/9 . 9/20 = 1/10

Vậy x = 1/10