\(\dfrac{3}{2}+\dfrac{7}{6}+\dfrac{13}{12}+...+\dfrac{73}{72}+\dfrac{91}{90}\)
=\(1+\dfrac{1}{2}+1+\dfrac{1}{6}+...+1+\dfrac{1}{72}+1+\dfrac{1}{90}\)
=\(\left(1+1+1+...+1\right)+\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{8.9}+\dfrac{1}{9.10}\)
=\(10+\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\)
=\(10+1-\dfrac{1}{10}\)
=\(10+\dfrac{9}{10}=\dfrac{109}{10}\)
Qua ib vs mk , mk sẽ mách cho bạn một cao thủ học rất giỏi toán !!!