Determine whether the following series converge or diverge. If the series converges, then determine its sum.
\sum_{k=0}^{\infty}\left(-\dfrac{3}{4}\right)^k
\sum_{k=0}^{\infty}\left(\dfrac{1}{2}\right)^k
\sum_{k=0}^{\infty}\left(\dfrac{3}{4}\right)^k
\sum_{k=0}^{\infty}\left(-\dfrac{7}{4}\right)^k
\sum_{k=0}^{\infty}\left(-1\right)^k
\sum_{k=0}^{\infty}\left(-\dfrac{7}{8}\right)^k
\sum_{k=0}^{\infty}\left(\dfrac{1}{4}\right)^k