## Thomas' Calculus 13th Edition

Let us consider $a_n=\dfrac{n^4}{(-4)^n}$ Also, $|a_n|=|\dfrac{n^4}{(-4)^n}|=\dfrac{n^4}{4^n}$ In order to solve the given series we will take the help of Ratio Test. This test states that when the limit $L \lt 1$ , the series converges and for $L \gt 1$, the series diverges. $L=\lim\limits_{n \to \infty} |\dfrac{a_{n+1}}{a_{n}} |=\lim\limits_{n \to \infty}|\dfrac{\dfrac{(n+1)^4}{4^{n+1}}}{\dfrac{n^4}{4^n}}|$ $\implies L=\dfrac{1}{4} \lt 1$ Hence, the series Converges by the ratio test.