Bài 5:
\(A=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}=1-\dfrac{1}{6}=\dfrac{5}{6}\\ B=1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{40}-\dfrac{1}{43}=1-\dfrac{1}{43}=\dfrac{42}{43}\)
Bài 6:
\(\Rightarrow\dfrac{4}{1.5}+\dfrac{4}{5.9}+\dfrac{4}{9.13}+\dfrac{4}{13.17}+\dfrac{4}{17.21}+x=\dfrac{6}{7}\\ \Rightarrow1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{17}-\dfrac{1}{21}+x=\dfrac{6}{7}\\ \Rightarrow1-\dfrac{1}{21}+x=\dfrac{6}{7}\\ \Rightarrow\dfrac{20}{21}+x=\dfrac{6}{7}\\ \Rightarrow x=\dfrac{6}{7}-\dfrac{20}{21}=-\dfrac{2}{21}\)
