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

Consider $u_n=(-1)^{n+1}\dfrac{n^2+5}{ n^2+4}$ Now $\lim\limits_{n \to \infty} u_n=\dfrac{n^2+5}{ n^2+4}=1$ $\lim\limits_{n \to \infty} (-1)^{n+1}\dfrac{n^2+5}{ n^2+4}=DNE$ Thus the series diverges by the nth Term Test for Divergence.