Question: State whether each of the following series converge or diverge. No reasons for your answers are necessary.

1. \(\sum\limits_{n=0}^{\infty }{{{\left( -1 \right)}^{n}}}\frac{{{4}^{n}}}{{{3}^{n}}}\)
2. \(\sum\limits_{n=0}^{\infty }{{{\left( -1 \right)}^{n}}}\frac{1}{1+\sqrt{n}}\)
3. \[\sum\limits_{n=0}^{\infty }{\frac{{{2}^{n}}+{{4}^{n}}}{{{5}^{n}}}}\]
4. \[\sum\limits_{n=0}^{\infty }{\frac{n\ln n}{{{\left( n+2 \right)}^{2}}}}\]
5. \(\sum\limits_{n=0}^{\infty }{\left( \frac{2}{n}-\frac{1}{n+1} \right)}\)

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