## University Calculus: Early Transcendentals (3rd Edition)

Consider $u_n=(-1)^{n+1}\dfrac{2^n}{ n^2}$ Here, $u_n$ is positive for all the values of $n$. Now $\lim\limits_{n \to \infty} u_n=(-1)^{n+1}\dfrac{2^n}{ n^2}=DNE$ The series diverges by the nth Term Test for Divergence.