\(B=\dfrac{7}{3\cdot4}+\dfrac{9}{4\cdot5}+\dfrac{11}{5\cdot6}+\dfrac{13}{6\cdot7}+\dfrac{15}{7\cdot8}+\dfrac{17}{8\cdot9}\)
\(=\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{5}+\dfrac{1}{6}+\dfrac{1}{6}+\dfrac{1}{7}+\dfrac{1}{7}+\dfrac{1}{8}+\dfrac{1}{8}+\dfrac{1}{9}\)
\(=\dfrac{4}{9}+\dfrac{1}{2}+\dfrac{2}{5}+\dfrac{1}{3}+\dfrac{2}{7}+\dfrac{1}{4}\)
=2789/1260