Let a_1=1 and for n ≥ 1, a_n+1=1/2 a_n+(n^2-2 n-1)/(n^2(n+1)^2). Then |Σ_n=1^∞(a_n-2/n^2)| is equal to ____.

Let $\displaystyle a_1=1$ and for $\displaystyle n \geqslant 1, a_{n+1}=\frac{1}{2} a_n+\frac{n^2-2 n-1}{n^2(n+1)^2}$. Then $\displaystyle \left|\sum_{n=1}^{\infty}\left(a_n-\frac{2}{n^2}\right)\right|$ is equal to $\displaystyle \_\_\_\_$.