$$ \sum_{n=1}^\infty \frac{(2-3)^{2n}}{n} $$ $$ = \sum_{n=1}^\infty \frac{(-1)^{2n}}{n} $$ $$ = \sum_{n=1}^\infty \frac{1}{n} $$

Diverges (\(p\)-power-series where \(p\leq1\)).

$$ \sum_{n=1}^\infty \frac{(4-3)^{2n}}{n} $$ $$ = \sum_{n=1}^\infty \frac{(1)^{2n}}{n} $$ $$ = \sum_{n=1}^\infty \frac{1}{n} $$

Diverges (\(p\)-power-series where \(p\leq1\)).