Question

Tính nhanh 1/42 + 1/30 + 1/20 + 1/12 + 1/6 = ?

Answer 1

1/42 + 1/30 +1/20 + 1/12 + 1/6

= 1/6+ 1/12 + 1/20 + 1/30 + 1/42

= 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7

= 1/2 - 1/3 + 1/3 -1/4 + 1 /4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7

= 1/2 - 1/7

= 5/14

Answer 2

\(\frac{1}{42}+\frac{1}{30}+\frac{1}{20}+\frac{1}{12}+\frac{1}{6}=\frac{1}{6\times7}+\frac{1}{5\times6}+\frac{1}{4\times5}+\frac{1}{3\times4}+\frac{1}{2\times3}\)

\(=\frac{1}{6}-\frac{1}{7}+\frac{1}{5}-\frac{1}{6}+\frac{1}{4}-\frac{1}{5}+\frac{1}{3}-\frac{1}{4}+\frac{1}{2}-\frac{1}{3}\)

\(=\frac{1}{2}-\frac{1}{7}=\frac{5}{14}\)