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Show whether the infinite series $$\frac{2+e^n}{3 + \pi^n}$$ is convergent or divergent.

Likely to be solved using comparison, ratio test or limit of partial sum.

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Hint: For all $n \geq 1$ $$ \frac{2 + e^n}{3+\pi ^n} < \frac{2+e^n}{\pi ^n} = \frac{2}{\pi^n} + \left( \frac{e}{\pi} \right)^n $$

Can you take it from here?

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