(Solved): A. [10 pts] Consider the geometric series below. \[ \frac{5}{2}+\frac{15}{8}+\frac{45}{32}+\ldots \ ...

A. [10 pts] Consider the geometric series below. \[ \frac{5}{2}+\frac{15}{8}+\frac{45}{32}+\ldots \] i. [5 pts] Write the series in summation notation. ii. [5 pts] Determine if the series converges or diverges and explain your response. If it converges, find its value. B. \( [10 \mathrm{pts}] \) Calculate \( \lim _{n \rightarrow \infty} n^{3 / \ln (n)} \)