Question

3/2 + 7/6 + 13/12 +.......+73/72

Giải chi tiết hộ mình

Answer 1

\(\frac{3}{2}+\frac{7}{6}+\frac{13}{12}+...+\frac{73}{72}\)

\(=1+\frac{1}{2}+1+\frac{1}{6}+1+\frac{1}{13}+...+1+\frac{1}{72}\)

\(=8+\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{72}\right)\)

\(=8+\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{8.9}\right)\)

\(=8+\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{8}-\frac{1}{9}\right)\)

\(=8+1-\frac{1}{9}=8\frac{8}{9}\)

Answer 2

\(\frac{3}{2}+\frac{7}{6}+\frac{13}{12}+...+\frac{73}{72}\)

\(=1+\frac{1}{2}+1+\frac{1}{6}+...+1+\frac{1}{72}\)

\(=\left(1+1+...+1\right)+\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{8.9}\right)\)

\(=8+1-\frac{1}{9}\)

\(=9-\frac{1}{9}=\frac{80}{9}\)