LCM of 6,12,20, and so on?

Algebra Level 3

$\dfrac{1}{1} - \dfrac{5}{6} + \dfrac{7}{12} - \dfrac{9}{20} + \dfrac{11}{30} - \dfrac{13}{42} + \dfrac{15}{56} - \dfrac{17}{72} + \dfrac{19}{90}$

If the expression above is in the form of $\frac a b$ for coprime positive integers $a,b$ , find $a+b$ ?