Convergence of $\sum_{n=1}^\infty\frac{1}{2\cdot n}$ It is possible to deduce the value of the following (in my opinion) converging infinite series? If yes, then what is it?
$$\sum_{n=1}^\infty\frac{1}{2\cdot n}$$
where n is an integer. Sorry if the notation is a bit off, I hope youse get the idea.

The series is not convergent, since it is half of the harmonic series which is known to be divergent$^1$.
$$\sum_{n=1}^{\infty }\frac{1}{2n}=\frac{1}{2}\sum_{n=1}^{\infty }\frac{1}{n}.$$
--
$^1$ The sum of the following $k$ terms is greater or equal to $\frac{1}{2}$
$$\frac{1}{k+1}+\frac{1}{k+2}+\ldots +\frac{1}{2k-1}+\frac{1}{2k}\geq
k\times \frac{1}{2k}=\frac{1}{2},$$
because each term is greater or equal to $\frac{1}{2k}$.
