$a_n={(-1)^{n+1}\dfrac{(n+1)^4}{4^n}}$ $\displaystyle\lim_{n\to\infty}\left|\, \frac{{{a}_{n+1}}}{{{a}_{n}}} \,\right|=$ [[☃ math-keypad 1]] **Based on your answer, what does the ratio test say about $S=\displaystyle\sum_{n=1}^{\infty}a_n$?** [[☃ radio 1]]