Question

Tính nhanh : 

              1/4+ 1/8+ 1/24+ 1/48+1/80+1/120+1/168

 

Answer 1

\(\frac{1}{4}+\frac{1}{8}+\frac{1}{24}+\frac{1}{48}+\frac{1}{80}+\frac{1}{120}+\frac{1}{168}\)

\(=\frac{1}{4}.\left(1+\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\right)\)

\(=\frac{1}{4}.\left(1+\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\right)\)

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

\(=\frac{1}{4}.\left(1+1-\frac{1}{7}\right)\)

\(=\frac{1}{4}.\left(2-\frac{1}{7}\right)\)

\(=\frac{1}{4}.\frac{13}{7}=\frac{13}{28}\)

Answer 2

Là 1 phần 4 + 1phan 8+ va cu nhu the