Problem 1115 (difficulty: 4/10)

Determine whether the following series are convergent or divergent.

\(\displaystyle \sum \left(1-\frac1n\right)^n \qquad \sum \left(1-\frac1n\right)^{n^2} \qquad \sum \left(\frac{n-1}{n+1}\right)^{\frac{n}2\log n+n\log\log n} \qquad \sum \frac{n^{n+\frac1n}}{\left(n+\frac1n\right)^n} \)

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