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 \(a+b\)?

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