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 ___________.

If the system of linear equations
$$2x - 3y = \gamma + 5$$,
$$\alpha x + 5y = \beta + 1$$, where $$\alpha$$, $$\beta$$, $$\gamma$$ $$\in$$ R has infinitely many solutions then the value
of | 9$$\alpha$$ + 3$$\beta$$ + 5$$\gamma$$ | is equal to ____________.

Let $$A = \left( {\matrix{ {1 + i} & 1 \cr { - i} & 0 \cr } } \right)$$ where $$i = \sqrt { - 1} $$. Then, the number of elements in the set { n $$\in$$ {1, 2, ......, 100} : Aⁿ = A } is ____________.

Sum of squares of modulus of all the complex numbers z satisfying $$\overline z = i{z^2} + {z^2} - z$$ is equal to ___________.