Will this series converge? $\sum \frac {1/2 + (-1)^n}{n}$

Question

Will this series converge? $\sum \frac {1/2 + (-1)^n}{n}$

MY Try: Dirichilet , Abel , libnitz rules can not be used. $\sum \frac {1/2 + (-1)^n}{n} = \sum \frac {1}{2n} + \sum\frac {(-1)^n}{2n} $. Is it possible to write in that way? If yes the how?

Can anyone please help me out?

Answer 1

$$\sum\frac{1/2+(-1)^n}{n}=\frac{1}{2}\sum\frac{1}{n}+\sum\frac{(-1)^n}{n}$$ I believe that the first summation is called the harmonic series and is divergent whilst the second summation is convergent