Bài 4:
\(A=\dfrac{1}{10.11}+\dfrac{1}{11.12}+...+\dfrac{1}{120.121}\\
=\dfrac{1}{10}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{12}+...+\dfrac{1}{120}-\dfrac{1}{121}\\
=\dfrac{1}{10}-\dfrac{1}{121}\\
=\dfrac{111}{1210}\)
\(B=\dfrac{1}{99}-\dfrac{1}{99.98}-\dfrac{1}{98.97}-...-\dfrac{1}{2.1}\\ =\dfrac{1}{99}-\dfrac{1}{99}+\dfrac{1}{98}-\dfrac{1}{98}+\dfrac{1}{97}-...-\dfrac{1}{2}+1\\ =1\)
Bài 5:
\(D=\dfrac{5^2}{1.6}+\dfrac{5^2}{6.11}+...+\dfrac{5^2}{26.31}\\
=5\left(\dfrac{5}{1.6}+\dfrac{5}{6.11}+...+\dfrac{5}{26.31}\right)\\
=5\left(1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{26}-\dfrac{1}{31}\right)\\
=5.\left(1-\dfrac{1}{31}\right)\\
=5.\dfrac{30}{31}=\dfrac{150}{31}\)
\(K=\dfrac{4}{11.16}+\dfrac{4}{16.21}+...+\dfrac{4}{61.66}\\ =\dfrac{4}{5}\left(\dfrac{5}{11.16}+\dfrac{5}{16.21}+...+\dfrac{4}{61.66}\right)\\ =\dfrac{4}{5}\left(\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{21}+...+\dfrac{1}{61}-\dfrac{1}{66}\right)\\ =\dfrac{4}{5}.\left(\dfrac{1}{11}-\dfrac{1}{66}\right)\\ =\dfrac{4}{5}.\dfrac{5}{66}\\ =\dfrac{2}{33}\)
