Consider the infinite series below. For each series, decide if it diverges, converges conditionally, or converges absolutely and justify your conclusion. State the test you used.

1. $\frac { 1 } { 3 } + \frac { 1 } { 6 } + \frac { 1 } { 11 } + \frac { 1 } { 18 } + \frac { 1 } { 27 } +$

   Step (a):

   $=\displaystyle\sum_{n=1}^\infty \frac{1}{n^2+2}$

2. $\frac { 1 } { 2 } + \frac { 1 } { 9 } + \frac { 1 } { 28 } + \frac { 1 } { 65 } + \frac { 1 } { 126 } + \frac { 1 } { 217 } +$

   Step (b):

   $=\displaystyle\sum_{n=1}^\infty \frac{1}{n^3+1}$

3. $\operatorname { ln } \frac { 1 } { 2 } + \operatorname { ln } \frac { 2 } { 3 } + \operatorname { ln } \frac { 3 } { 4 } + \ldots$

   Step (c):

   $= \ln(1)-\ln(2)+\ln(2)-\ln(3)+\ln(3)-\ln(4)+...$

4. $- 2 + 1 - \frac { 2 } { 3 } + \frac { 1 } { 2 } - \frac { 2 } { 5 } + \ldots$

   Hint (d):

   Think of this as two separate series:
   $\frac{-2}{1}+\frac{-2}{3}+\frac{-2}{5}+...\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+...$