lim-n-U-n-1-Un-gt-0-Test-for-convergence-

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

l i \underset{n - \infty}{m} / \frac{U_{n} + 1}{U n} / > 0

T e s t f o r c o n v e r g e n c e

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

test for convergence states that

if U_{n} is a sequence and

∙ \lim_{x \to \infty} ∣ \frac{U_{n + 1}}{U_{n}} ∣ > 1 \Rightarrow U_{n} is divergent .

∙ \lim_{x \to \infty} ∣ \frac{U_{n + 1}}{U_{n}} ∣ < 1 \Rightarrow U_{n} is convergent .

∙ \lim_{x \to \infty} ∣ \frac{U_{n + 1}}{U_{n}} ∣ = 1 \Rightarrow inconclusive