a) $\dfrac{1}{3}-\dfrac{2}{15}+\dfrac{3}{35}-\dfrac{4}{63}+\dfrac{5}{99}-\dfrac{6}{143} $
$=\dfrac{1}{1.3} -\dfrac{2}{3.5}+\dfrac{3}{5.7}-\dfrac{4}{7.9}+\dfrac{5}{9.11}-\dfrac{6}{11.13} $
$=1-\dfrac{2}{3}-\dfrac{1}{3}+\dfrac{1}{5} +\dfrac{3}{10}-\dfrac{3}{14}-\dfrac{2}{7}+\dfrac{2}{9}+\dfrac{5}{18}-\dfrac{5}{22}-\dfrac{3}{11}+\dfrac{3}{13}$
$=\dfrac{3}{13}$
