\(A=\dfrac{1}{1.2}+\dfrac{1}{3.4}+\dfrac{1}{5.6}+...+\dfrac{1}{99.100}\)

\(A=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{99}-\dfrac{1}{100}\)

\(A=1-\dfrac{1}{100}\)

\(A=\dfrac{1}{99}\)

\(Vì:\dfrac{1}{99}< 1\)

=>\(A< 1\)

a)\(\dfrac{5}{4}-\left(\dfrac{1}{2}\right)^2=\dfrac{5}{4}-\dfrac{1}{4}=\dfrac{4}{4}=4\)

b)\(\dfrac{2}{3}.\dfrac{-3}{2}+\dfrac{-7}{2}.\dfrac{2}{3}=\dfrac{2}{3}.\left(\dfrac{-3}{2}+\dfrac{-7}{2}\right)=\dfrac{2}{3}.\dfrac{-10}{2}=\dfrac{-20}{6}=\dfrac{-10}{3}\)

c)\(\left(\dfrac{1}{5}+\dfrac{4}{13}\right)+\left(\dfrac{-2}{5}+\dfrac{7}{13}\right)-\left(\dfrac{4}{5}-\dfrac{2}{13}\right)=\dfrac{1}{5}+\dfrac{4}{13}+\dfrac{-2}{5}+\dfrac{7}{13}-\dfrac{4}{5}+\dfrac{2}{13}=\dfrac{1}{5}+\dfrac{-2}{5}-\dfrac{4}{5}+\dfrac{4}{13}+\dfrac{7}{13}+\dfrac{2}{13}=-1+1=0\)