Làm cái phép trong ngoặc:
=1/3 . (1/4-1/9+1/9-...-1/49)
=1/3 . (1/4-1/49)
Xong tự tính nốt 🙃
\(A=\left(\dfrac{1}{4\cdot9}+\dfrac{1}{9\cdot14}+...+\dfrac{1}{44\cdot49}\right)\cdot\dfrac{1-3-5-7-...-49}{89}\)
Đặt B=3+5+7+...+49
Số số hạng là (49-3):2+1=46:2+1=24(số)
=>B=(49+3)*24/2=624
\(A=\dfrac{1-624}{89}\cdot\dfrac{1}{5}\cdot\left(\dfrac{5}{4\cdot9}+\dfrac{5}{9\cdot14}+...+\dfrac{5}{44\cdot49}\right)\)
\(=\dfrac{-623}{89}\cdot\dfrac{1}{5}\left(\dfrac{1}{4}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{14}+...+\dfrac{1}{44}-\dfrac{1}{49}\right)\)
\(=-\dfrac{7}{5}\cdot\left(\dfrac{1}{4}-\dfrac{1}{49}\right)=\dfrac{-7}{5}\cdot\dfrac{45}{196}=\dfrac{-7}{196}\cdot\dfrac{45}{5}\)
\(=-\dfrac{9}{28}\)
