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

Algebra Level 3

1156+712920+11301342+15561772+1990 \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 ab \frac a b for coprime positive integers a,ba,b, find a+ba+b?

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