Math Problem Solver

CALCULATE AND determine whether each series is either 1. absolutely convergent 2. converges, but is not absolutely convergent or 3. diverges.

1. \sum_{n=1}^{\infty} \frac{(n+1)^n}{5^n} ]

2. \sum_{n=1}^{\infty} (-1)^{n+1} \frac{(5+n)3^n}{(n^2)3^{2n}} ]

3. \sum_{n=1}^{\infty} \left( \frac{n^4}{2 - 6n^3} \right)^n ]

4. \sum_{n=1}^{\infty} \frac{(-2n)^n}{n^3} ]

5. \sum_{n=1}^{\infty} \frac{(n+1)^n}{5n^2} ]

6. \sum_{n=1}^{\infty} (-1)^n n^{n-2} \ln(n+4) ]