Real series/Quotient/Convergence/Quotient criteria/Exercise

Let $\sum _{n=0}^n{a}_n$ be a real series with $a_n\ne 0$ for all $n$. Suppose that the sequence of fractions

$x_n=\frac{a_{n+1}}{a_n}$

converge to a real number $x$ with $-1<x<1$. Show, using the ratio test, that the series converges.

Create a solution