Tham khảo
A=3/2+7/6+13/12+...+91/90
A=1+1/2+1+1/6+…+1+1/72+1+1/90
A=(1+1+1+…+1+1)+1/1.2+1/2.3+1/3.4+…+1/9.10
A=10+1/1-1/2+1/2-1/3+…-1/9+1/9+1/10
A=10+1-1/10
A=10+9/10
A=109/10
\(S=\dfrac{3}{2}+\dfrac{7}{6}+\dfrac{13}{12}+...+\dfrac{91}{90}\)
\(=1+\dfrac{1}{2}+1+\dfrac{1}{6}+1+\dfrac{1}{12}+...+1+\dfrac{1}{90}\)
\(=\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{9.10}\right)+9\)
\(=\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{9}-\dfrac{1}{10}\right)+9\)
\(=1-\dfrac{1}{10}+9=\dfrac{99}{10}\)