Use ratio test to test for convergence or divergence

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I have online hw and it tells me if my answer is correct or not. It said that my answer for this problem is incorrect:

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Can someone tell me what I did wrong?

Also I might be asking alot of these questions later since I am new to this concept.

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If $\lim_{n\to\infty}a_{n+1}/a_n<1$ the series converges, if $\lim_{n\to\infty}a_{n+1}/a_n>1$ the series diverges.

The test gives no information if $\lim_{n\to\infty}a_{n+1}/a_n=1$.

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There are many mistakes.

  1. The series in not equal to the limit in the first line.

  2. Limit of the ratio of in the second line is probably from de l'Hospital's rule, but $n$ is discrete.

  3. If this limits is equal to 2, the series diverges (d'Alembert test).