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Question Number 31705 by gunawan last updated on 12/Mar/18

$$\mathrm{Given}\mathrm{sequence}\left(x_n\right)\mathrm{with}0<a=x_1<x_2=b$$ $$x_{n+1}=x_{n+1}+x_n,n=1,2,3,...$$ $$\mathrm{review}\mathrm{sequence}\left(r_n\right)\mathrm{with}{r}_n=\frac{x_{n+1}}{x_n},n=1,2,3,...$$ $$\mathrm{a}.\mathrm{Prove}\mathrm{that}1<r_n<2\mathrm{for}n=2,3,4,...$$ $$\mathrm{b}.\mathrm{Diverge}\mathrm{or}\mathrm{converge}\mathrm{is}\mathrm{the}\mathrm{squence}?$$

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