$\sum_{n=1}^{\infty} a_{2n-1}$ must converge

$\sum_{n=1}^{\infty} a_{2n-1} < \sum_{n=1}^{\infty} a_n$ (the odd-sum is less than the total sum)

$\sum_{n=1}^{\infty} a_{2n-1}$ could diverge

$\sum_{n=1}^{\infty} a_{2n-1} \leq \sum_{n=1}^{\infty} a_n$