Let the sum of the following infinite sequence be $N$. $1,\dfrac{1}{2},\dfrac{1}{2},\dfrac{1}{6},\dfrac{1}{4},\dfrac{1}{12},\dfrac{1}{8},\dfrac{1}{20},\dfrac{1}{16},\dfrac{1}{30},\dfrac{1}{32},\dfrac{1}{42} \ldots \ .$ Find the $\textbf{remainder}$ when $\displaystyle \Bigl(N^{2014}+1\Bigr)$ is divided by $\color{Purple}{\textbf{11}}$.

**Hint**:- Is it really $\textbf{a}$ sequence?

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