Chapter 11 - Section 11.2 - Series - 11.2 Exercises - Page 716: 34

Diverges

$\lim _{n\rightarrow \infty }\dfrac {2^{n}+4^{n}}{e^n}=\lim _{n\rightarrow \infty }\left( \left( \dfrac {2}{e}\right) ^{n}+\left( \dfrac {4}{e}\right) ^{n}\right) =\infty \left( 4 > e\right) \Rightarrow \sum ^{\infty }_{n=1}\dfrac {2^{n}+4^{n}}{e^n}$. Diverges