Let for n =1,2, …., 50, S_n be the sum of the infinite geometric progression whose first term is n^2 and whose common ratio is 1/(( n +1)^2). Then…

Let for $\displaystyle \mathrm{n}=1,2, \ldots ., 50, \mathrm{~S}_{\mathrm{n}}$ be the sum of the infinite geometric progression whose first term is $\displaystyle \mathrm{n}^2$ and whose common ratio is $\displaystyle \frac{1}{(\mathrm{n}+1)^2}$. Then the value of $\displaystyle \frac{1}{26}+\sum_{n=1}^{50}\left(\mathrm{~S}_n+\frac{2}{\mathrm{n}+1}-\mathrm{n}-1\right)$ is equal to \_\_\_\_.