# Limits involving Euler-Mascheroni Constant!

Calculus Level 5

$\large{\lim_{n \to \infty} \left( \left( \sum_{i=1}^{2n} \dfrac{(-1)^{i-1}}{i} {2n \choose i} \right) - \ln(8n) \right)}$

If the limit above can be expressed as $$\gamma - \ln(A)$$ for positive integer $$A$$, and where $$\gamma$$ is the Euler-Mascheroni's Constant, find $$A$$.

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