= Solution
{c}
Let $u(x)=(\log x)x^{-2/3}$. Its <derivative> is
$$
u'(x)=x^{-5/3}\left(1-\frac23\log x\right),
$$
which is negative for $x>e^{3/2}$. Also $u(x)\to0$, since a positive power eventually dominates the <natural logarithm>. Thus the <alternating series test> proves convergence of $\sum(-1)^n u(n)$.
For $n\geq3$, $u(n)\geq n^{-2/3}$, whose <p-series> diverges. The <comparison test> therefore rules out <absolute convergence>. The answer is \b[conditional convergence].
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