\[ \large \lim_{n\to\infty} \left[ \left( \dfrac {2n}{2n^2-1} \cos \left( \dfrac{n+1}{2n-1}\right)\right) - \left( \dfrac n{1-2n} \cdot \dfrac {n(-1)^n}{n^2+1}\right) \right ] = \, ? \]

Note: Take the limit over the integers.

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