-working in real numbers, true or false? proof or counterexample:

(a) If $\displaystyle a_n$ is decreasing sequence of positive numbers, and $\displaystyle na_n \rightarrow 0$ as $\displaystyle n \rightarrow \infty$, then $\displaystyle \sum a_n$ converges.

(b)If $\displaystyle \sum a_n$ converges, then $\displaystyle \sum \frac{a_n}{\sqrt{n}} $converges.

(c)If $\displaystyle \sum a_n$ converges, then $\displaystyle \sum \frac{|a_n|}{n}$ converges.

(d)If $\displaystyle \sum a_n$ converges, then $\displaystyle \sum \frac{|a_n|}{n^{3/2}} $converges.