Discuss the convergence or divergence of the series
$$1) \sum_{n=1}^\infty \frac{1}{2n}$$ $$2) \sum_{n=1}^\infty \frac{1}{2n-1}$$ $$3) \sum_{n=1}^\infty \frac{2}{n^2+3}$$
I have three following partial sums, and I wanted to discuss whether it converges or diverges using comparison test, that is
Suppose $|a_n| \le b_n$ for every $n \sum_{n=1}^\infty b_n$ converges, then $\sum_{n=1}^\infty a_n$ converges
Suppose $0 \le b_n \le a_n$ for every $n \sum_{n=1}^\infty b_n$ diverges, then $\sum_{n=1}^\infty a_n$ diverges
So by using this definition, I have come to the solution for 1) that
$$A) \sum_{n=1}^\infty \frac{1}{2n} = \frac12+\frac14+\frac16+....$$ where $$B) \sum_{n=1}^\infty \frac{1}{n} = 1+\frac12+\frac13+....$$
and since B is bigger than A, we say this partial sums diverge.
However, for 2) denominator is $2n-1$ and this gives me a headache.. also for 3)
Could I get some help solving these 2,3??