JEE Math Practice Question
Let Sn = 1 . (n $$-$$ 1) + 2 . (n $$-$$ 2) + 3 . (n $$-$$ 3) + ..... + (n $$-$$ 1) . 1, n $$\ge$$ 4. The sum $$\sum\limits_{n = 4}^\infty {\left( {{{2{S_n}} \over {n!}} - {1 \over {(n - 2)!}}} \right)} $$ is equal to :
- A.$${{e - 1} \over 3}$$
- B.$${{e - 2} \over 6}$$
- C.$${e \over 3}$$
- D.$${e \over 6}$$
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