MATHEMATICS_Q19_JEE_Advanced_2010_S1 - Competishun – Live JEE & NEET Courses and Exam Prep

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JEE ADVANCE 2010

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Let $S_k, k=1,2, \ldots ., 100$, denote the sum of the infinite geometric series whose first term is $\frac{k-1}{k!}$ and the common ratio is $\frac{1}{k}$. Then the value of $\frac{100^2}{100!}+\sum_{k=1}^{100}\left|\left(k^2-3 k+1\right) S_k\right|$ is

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