\(\dfrac{3}{2}xA=\dfrac{3}{1x4}+\dfrac{3}{4x7}+\dfrac{3}{7x10}+...+\dfrac{3}{97x100}=\)
\(=\dfrac{4-1}{1x4}+\dfrac{7-4}{4x7}+\dfrac{10-7}{7x10}+...+\dfrac{100-97}{97x100}=\)
\(=1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{97}-\dfrac{1}{100}=\)
\(=1-\dfrac{1}{100}=\dfrac{99}{100}\Rightarrow A=\dfrac{99}{100}x\dfrac{2}{3}=\dfrac{33}{50}\)