Quadruple Sum

Calculus Level 5

S=i=1j=1k=1l=1(1)i+j+k+li+j+k+l=log(a)abS=\sum_{i=1}^{\infty}\sum_{j=1}^{\infty}\sum_{k=1}^{\infty}\sum_{l=1}^{\infty}\dfrac{(-1)^{i+j+k+l}}{i+j+k+l}=\log(a)-\dfrac{a}{b} a,ba,b are co-prime positive integers. Find a+ba+b.

NOTE : SS does converge.

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