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My task is to find sequences $c_n, d_n$ such that $(1-\frac{1}{c_nx+d_n+1})^n \rightarrow e^{-(1+x)}$. My attempt was to rewrite $e^{-(1+x)}$ in limit form as $(1-\frac{1+x}{n})^n$ and compare coefficients, but this doesn't work. Appreciate any hints!

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