Question

1/2+5/6+11/12+19/20+29/30+41/42 = ?

Answer 1

\(\frac{1}{2}+\frac{5}{6}+\frac{19}{20}+\frac{29}{30}+\frac{41}{42}\)

\(=\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{6}\right)+\left(1-\frac{1}{12}\right)+\left(1-\frac{1}{20}\right)+\left(1-\frac{1}{30}\right)+\left(1-\frac{1}{42}\right)\)

\(=\left(1+1+1+1+1+1\right)-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\right)\)

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

\(=6-\left(1-\frac{1}{7}\right)=6-\frac{6}{7}=\frac{36}{7}\)

Answer 2

thì quy đồng lên mẫu là 420 rồi cộng với nhau ý bạn

Answer 3

\(\frac{36}{7}\)