Let Sk,k=1,2,,100, denotes thesum of the infinite geometric series whose first term s k!k−1 and the common ratio is k1 , then the value of 100!1002+k=1∑100(k2−3k+1)Sk is _______.

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Let {S}_{{k}},{k}={1},{2},,{100}, denotes thesum of the infini

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Let $S_{k}, k = 1, 2,, 100,$ denotes thesum of the infinite geometric series whose first term s $\frac{k - 1}{k !}$ and the common ratio is $\frac{1}{k}$ , then the value of $\frac{100 ^{2}}{100 !} + k = 1 \sum 100 (k^{2} - 3 k + 1) S_{k}$ is _______.

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Let

S_{k}, k = 1, 2,, 100,

denotes thesum of the infinite geometric series whose first term s

\frac{k - 1}{k !}

and the common ratio is

\frac{1}{k}

, then the value of

\frac{100 ^{2}}{100 !} + k = 1 \sum 100 (k^{2} - 3 k + 1) S_{k}

is _______.

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Question Text

Let

S_{k}, k = 1, 2,, 100,

denotes thesum of the infinite geometric series whose first term s

\frac{k - 1}{k !}

and the common ratio is

\frac{1}{k}

, then the value of

\frac{100 ^{2}}{100 !} + k = 1 \sum 100 (k^{2} - 3 k + 1) S_{k}

is _______.