Question```latex \text{Part I-Write the most simplified form of your answer in the space provided (3 points)}
\text{a) Determine whether the following sequence converges or diverges.}
\text{a. } \sum_{n=0}^{\infty} \frac{2^{2}}{(x+1)^{2}} \text{ is } \qquad
\text{b. } \sum_{n=1}^{\infty} \frac{3}{n^{2}-3n+2} \text{ is } \qquad
\qquad \text{convergent, or divergent} \qquad
\text{1. For what values of } x \text{ does the series } \sum_{n=0}^{\infty} n x^{n} \text{ converge?} \qquad
\text{Part II: Work out each of the following clearly and neatly showing all the necessary steps: (4 points each)}
\text{5. Determine if the following series converges or diverges.}
\text{a. } \sum_{i=3}^{\infty}\left(1-\frac{3}{n}\right) m^{2} \text{ by root test.}
\text{b. } \sum^{\infty}=\frac{n}{\sqrt{\pi^{2}-12}} \text{ by comparison test.} ```