Solution
= Solution
{c}
\b[The implication is true, with <absolute convergence>.] Since $n^{3/2}a_n\to0$, there is $N$ such that $|a_n|\leq n^{-3/2}$ for $n\geq N$. The <p-series> $\sum n^{-3/2}$ converges because its exponent exceeds one. The <comparison test> proves $\sum|a_n|<\infty$, and <absolute convergence> implies convergence of $\sum a_n$.