[Solved] Let S_k = 1, 2, .... 100, denote the sumof the infinite geometric series whose first term is \\frac{k-1}{k!} and the common ratio is \\frac{1}{k}. Then the value of \\frac{100^2}{100!}+\\sum_{k=1}^{100}\\mid (k^2 - 3k + 1)S_k \\mid is - - JEE (Advanced) 2010 Paper-1