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Let Sn = 1 (n - 1) + 2. (n -2) + 3. (n ...

Let `S_n = 1 (n - 1) + 2. (n -2) + 3. (n - 3) +…+ (n -1).1, n ge 4.`
The sum `sum_(n = 4)^oo ((2S_n)/(n!) - 1/((n - 2)!))` is equal to :

A

`(e - 2)/6`

B

`e/3`

C

`(e-1)/3`

D

`e/6`

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