Consider the Series $\frac{1}{3}+\frac{2}{5}+\frac{3}{7}+\frac{4}{9}+\frac{5}{11}+\ldots$ (A)Find a Formula for the General Term $s_{n}, n \geq 1$

Essay

Consider the series: $\frac{1}{3}+\frac{2}{5}+\frac{3}{7}+\frac{4}{9}+\frac{5}{11}+\ldots$
(a)Find a formula for the general term $s_{n}, n \geq 1$ .
(b)Find the partial sums $S_{1}, S_{2}, S_{3}, S_{4}, S_{5}$ .
(c)Use your result from part (b)to predict the limit of the partial sums, $\lim _{n \rightarrow \infty} S_{n}$ .Does this indicate that the series converges or diverges?