Answer
Please see step-by-step.
Work Step by Step
The given sequence can be rewritten (for easier pattern recognition) as
$\displaystyle \frac{3}{3},\ \displaystyle \frac{3}{5},\ \displaystyle \frac{3}{7},\ \displaystyle \frac{3}{9},\ \displaystyle \frac{3}{11},\ ...$
The reciprocals form a sequence
$\displaystyle \frac{3}{3},\ \displaystyle \frac{5}{3},\ \displaystyle \frac{7}{3},\ \displaystyle \frac{9}{3},\ \displaystyle \frac{11}{3},\ ...$
which we recognize to be arithmetic, because it has a common difference,
$d=\displaystyle \frac{2}{3}.$
The reciprocals form an arithmetic sequence,
so the original sequence is harmonic.
