$\sum_{n=1}^{\infty} \frac{(1/2) + (-1)^{n}}{n}$ converges or diverges? How to check if the series $$\sum_{n=1}^{\infty} \frac{(1/2) + (-1)^{n}}{n}$$ converges or diverges?
When $n$ is odd, series is $\sum \frac{-1}{2n}$
When $n$ is even, series is $\sum \frac{3}{2n}$
This series is similar to the series 
$$\sum \frac{-1}{2(2n-1)} + \frac{3}{2(2n)}$$
$$= \sum \frac{8n-6}{8n(2n-1)}$$
Which is clearly divergent.
So, the given series is divergent.
Is this method right?
Please, suggest if there is some easier way.

hint
$$\sum \frac{(-1)^n}{n}$$
is convergent by  alternate criteria.
$$\frac 12\sum \frac 1n$$
is a divergent Riemann series.
The sum of a convergent and a divergent series is a Divergent one.
