Let S_k, k = 1, 2, … , 100, denote the sum of the infinite geometric series whose first term is \frac{k-1}{k!} and the common ratio is 1/k. Then the value of {100}^2/{100!} + \sum^{100}_{k=1}|(k^2-3k+1)S_k| is ____. [JEE Adv 2010 P1]

Sequences and Series

Section: Mathematics

Question : 19 of 22

Marks: +1, -0

Let Sk, k = 1, 2, … , 100, denote the sum of the infinite geometric series whose first term is

k−1

and the common ratio is

. Then the value of

1002

100!

100

k=1

|(k2−3k+1)Sk| is ____.

[JEE Adv 2010 P1]

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