QUESTION $2$

The series ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{2e^n}{e^{2n}+2}$

A$.$ converges necessarily to the same value of the integral ${\displaystyle \underset{1}{\overset{}{}}}\frac{2e^x}{e^{2x}+2}dx$

B$.$ is convergent by the integral test

C$.$ diverges because ${\displaystyle \underset{1}{\overset{}{}}}\frac{2e^x}{e^{2x}+2}dx=$

D$.$

diverges because the derivative of the function $f(x)=\frac{2e^x}{e^{2x}+2}$ is positive

E$.$ is divergent by the integral test