Hi,
The following series is convergent for the values of x?
thanks
The ratio test states that the series will be convergent where $\displaystyle \displaystyle \begin{align*} \left|\frac{a_{n+1}}{a_n}\right| < 1 \end{align*}$, divergent where $\displaystyle \displaystyle \begin{align*} \left|\frac{a_{n+1}}{a_n}\right| > 1 \end{align*}$, and inconclusive where $\displaystyle \displaystyle \begin{align*} \left|\frac{a_{n+1}}{a_n}\right| = 1 \end{align*}$. So a good place to start would be to evaluate where this ratio is less than 1.