Sequences And Series

Let for n = 1, 2, ......, 50, S_n be the sum of the infinite geometric progression whose first term is n² and whose common ratio is \({1 \over {{{(n + 1)}^2}}}\). Then the value of

\({1 \over {26}} + \sum\limits_{n = 1}^{50} {\left( {{S_n} + {2 \over {n + 1}} - n - 1} \right)}\) is equal to ___________.