For each $\displaystyle y \in (0,1]$, find a series of the form $\displaystyle \sum\limits_{n=1}^{\infty}{a_nn^{-x}}$ which is absolutely convergent for $\displaystyle x>1$ but not for $\displaystyle x<1$ and is (conditionally) convergent for $\displaystyle x>y$ but not for $\displaystyle x<y$.