# Some sum reciprocal

Level pending

Let $$f$$ be a function such that

$$$$f(x)=\displaystyle \sum_{k=0}^\infty {\frac {k+1}{x^k}}$$$$

If $$f(-161)=S$$, what value of $$x$$ satisfies $$f(x) = \frac{1}{S}$$?

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