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Question
Simplify `1/("n"!) - 1/(("n" - 1)!) - 1/(("n" - 2)!)`
Solution
`1/("n"!) - 1/(("n" - 1)!) - 1/(("n" - 2)!)`
= `1/("n"("n" - 1)("n" - 2)!) - 1/(("n" - 1)("n" - 2)!) - 1/(("n" - 2)!)`
= `1/(("n" - 2)!) [1/("n"("n" - 1)) - 1/(("n" - 1)) - 1]`
= `1/(("n" - 2)!) [(1 - "n" - "n"("n" - 1))/("n"("n" - 1))]`
= `(1 - "n"^2)/("n"("n" - 1)("n" - 2)!)`
= `(-("n" - 1)("n" + 1))/("n"("n" - 1)("n" - 2)!)`
= `(-("n" + 1))/("n"("n" - 2)!)`
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