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Let n be a positive integer with f(n) = ...

Let `n` be a positive integer with `f(n) = 1! + 2! + 3!+.........+n! and p(x),Q(x)` be polynomial in `x` such that `f(n+2)=P(n)f(n+1)+Q(n)f(n)` for all `n >= 1,` Then
(a) `P(x) = x+3`
(b) `Q(x) = -x-2`
(c) `P(x) = -x-2`
(d) `Q(x) = x+3`

Text Solution

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The correct Answer is:
P(x)=x+3 and Q(x)=-x-2
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