# Difficult limits

Calculus Level 4

Let $$f\left(x\right) = {x^{n+2} + a_1 x^{n+1} + ... + a_{n+1} x + 1}$$, and $$g(x) = \frac{f\left(x\right)}{\left(x+1\right)^{n+1}}$$, where $$n \geq 0$$ is an integer, and $$x$$, $$a_1$$, ..., $$a_{n+1}$$ are real numbers

Find the sum of all possible values of $$\displaystyle \lim_{x \to 1} g(x)$$ when $$\displaystyle \lim_{x \to -1} g(x)$$ is defined, and $$\frac{d}{dx} f(-1) = \frac{d^2}{d^2 x} f(-1) = \cdots = \frac{d^{n+1}}{d^{n+1} x} f(-1)$$

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