11 is really lovely, we'll bring it everywhere!

Calculus Level 3

Let the sum of the following infinite sequence be NN. 1,12,12,16,14,112,18,120,116,130,132,142 .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 remainder\textbf{remainder} when (N2014+1)\displaystyle \Bigl(N^{2014}+1\Bigr) is divided by 11\color{Purple}{\textbf{11}}.


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

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