# Does this series diverge or converge?

by Anton   Last Updated November 08, 2018 23:20 PM

Does this serie diverge or converge ? Why ?

$$\sum \frac{\sqrt{n^3}+e^{-n}}{\sqrt{n^5}+\pi}$$

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HINT

The key fact is that

$$\frac{\sqrt{n^3}+e^{-n}}{\sqrt{n^5}+\pi}\sim \frac1n$$

then refer to limit comparison test with $$\sum \frac1n$$.

gimusi
November 08, 2018 22:43 PM