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I need to prove that

$$ \sum_{n=0}^{\infty} \left(\exp\left(\frac{n^2+2n}{n^2+1} \right) - e \right) $$

diverges. The solution suggests using the limit comparison test, but since we didn't

cover that in my class I was wondering if there is some other easy way to prove divergence.

Thank you for your help.

Vincent

$$ \sum_{n=0}^{\infty} \left(\exp\left(\frac{n^2+2n}{n^2+1} \right) - e \right) $$

diverges. The solution suggests using the limit comparison test, but since we didn't

cover that in my class I was wondering if there is some other easy way to prove divergence.

Thank you for your help.

Vincent

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