  We consider an extension of the Ramanujan series with a variable $x$. If we
let $x=x_0$, we call the resulting series: "Ramanujan series with the shift
$x_0$". Then, we relate these shifted series to some $q$-series and solve the
case of level $4$ with the shift $x_0=1/2$. Finally, we indicate a possible way
towards proving some patterns observed by the author corresponding to the
levels $\ell=1, 2, 3$ and the shift $x_0=1/2$.
