Let $\{a_n\}$ be a sequence of real numbers. which one of the following is always true?
(a)$\sum a_n$ converges, then $\sum a_n^4$ converges.
(b)$\sum |a_n|$ converges, then $\sum a_n^2$ converges.
(c)$\sum a_n$ diverges, then $\sum a_n^3$ diverges.
(d)$\sum |a_n|$ diverges, then $\sum a_n^2$ diverges.
$\sum a_n$ converges $\implies lim_{n\rightarrow \infty}a_n=0$, But this won't help here. I know the fact that converse of the Ratio test, root test,...etc need not true.
(c)$a_n=\frac{1}{n}$ $\implies$ the statement is false.
(d)$a_n=\frac{(-1)^n}{n}$ $\implies$ the statement is false.
I am not able to judge (a) and (b). please help me.