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Sequences and Series question

2010 · Shift 1 · Q34

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JEE Advanced
Mathematics
Sequences and Series
2010 · Shift 1 · Q34

Sequences and Series question

2010 · Shift 1 · Q34

JEE AdvancedMathematicsSequences and SeriesNumerical+4 / −1

Let

{S_k}

= 1, 2,....., 100, denote the sum of the infinite geometric series whose first term is

\,{{k - 1} \over {k\,!}}

and the common ratio is

{1 \over k}

. Then the value of

{{{{100}^2}} \over {100!}}\,\, + \,\,\sum\limits_{k = 1}^{100} {\left| {({k^2} - 3k + 1)\,\,{S_k}} \right|\,\,}

is

Numerical answer

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