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11+12−13−14+15+16−17−18+⋯\large \dfrac{1}{1}+\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{6}-\dfrac{1}{7}-\dfrac{1}{8}+\cdots11+21−31−41+51+61−71−81+⋯
If the closed form of the sum above can be expressed as π+ln(a)a\dfrac{\pi+\ln (a)}{a}aπ+ln(a), where aaa is a positive integer, find aaa.
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