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

Given: $\Sigma_{n =1}^{\infty} \dfrac{e^n}{e^n+n}$ Thus, we have: $\lim\limits_{n \to \infty} \dfrac{e^n}{e^n+n}= \dfrac{\lim\limits_{n \to \infty} 1}{\lim\limits_{n \to \infty}(1+\dfrac{n}{e^n})}=\dfrac{\lim\limits_{n \to \infty} 1}{\lim\limits_{n \to \infty} 1+ \lim\limits_{n \to \infty}\dfrac{n}{e^n}}=\dfrac{1}{1+0}=1\ne 0$ Hence, the series is divergent as per the nth-term integral test.