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Question Number 85708 by Roland Mbunwe last updated on 24/Mar/20

$$li\underset{n-\mathrm{\infty }}{m}/\frac{U_n+1}{Un}/>0$$$$Testforconvergence$$

Answered by Rio Michael last updated on 24/Mar/20

$$\mathrm{test}\mathrm{for}\mathrm{convergence}\mathrm{states}\mathrm{that}$$$$\mathrm{if}{U}_n\mathrm{is}\mathrm{a}\mathrm{sequence}\mathrm{and}$$$$\bullet \underset{x\to \mathrm{\infty }}{\lim }\mid \frac{U_{n+1}}{U_n}\mid >1\Rightarrow U_n\mathrm{is}\mathrm{divergent}.$$$$\bullet \underset{x\to \mathrm{\infty }}{\lim }\mid \frac{U_{n+1}}{U_n}\mid <1\Rightarrow U_n\mathrm{is}\mathrm{convergent}.$$$$\bullet \underset{x\to \mathrm{\infty }}{\lim }\mid \frac{U_{n+1}}{U_n}\mid =1\Rightarrow \mathrm{inconclusive}$$

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