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nice one (precalculus)

Source: flanders '91

September 27, 2005
limitalgebrapolynomial

Problem Statement

(a) Show that for every n∈Nn\in\mathbb{N} there is exactly one x∈R+x\in\mathbb{R}^+ so that xn+xn+1=1x^n+x^{n+1}=1. Call this xnx_n. (b) Find lim⁡n→+∞xn\lim\limits_{n\rightarrow+\infty}x_n.
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