# Who's up to the challenge? 35

Calculus Level pending

$\large \displaystyle\lim _{ x\rightarrow \infty }{ \left( (f(x+2)\Gamma (x+2))^{ 1/(x+1) }-(f(x+1)\Gamma (x+1))^{ 1/x } \right) } =A{ e }^{ -B }$

Let $$f$$ be a polynomial whose coefficient in the leading term is positive and it satisfy the equation above for positive integers $$A$$ and $$B$$. Find $$A+B$$.

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