Question

Tính:

\(\dfrac{1}{3}+\)\(\dfrac{3}{7}+\dfrac{1}{7.2}+\dfrac{5}{2.13}+\dfrac{3}{13.4}+\dfrac{5}{4.21}\)

Answer 1

\(\dfrac{1}{3}+\dfrac{3}{7}+\dfrac{1}{2\cdot7}+\dfrac{5}{2\cdot13}+\dfrac{3}{13\cdot4}+\dfrac{5}{4\cdot21}\)

\(=\dfrac{1}{3}+\dfrac{3}{7}+\dfrac{1}{14}+\dfrac{5}{84}+\dfrac{5}{26}+\dfrac{3}{42}\)

\(=\dfrac{1}{3}+\dfrac{3}{7}+\dfrac{1}{14}+\dfrac{5}{84}+\dfrac{3}{42}+\dfrac{5}{26}\)

\(=\dfrac{28+36+6+5+6}{84}+\dfrac{5}{26}\)

\(=\dfrac{5}{26}+\dfrac{81}{84}\)

\(=\dfrac{5}{26}+\dfrac{27}{28}=\dfrac{421}{364}\)