For what values of $p$ will both series $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ^ { 2 p } }$ and $\sum _ { n = 1 } ^ { \infty } \left( \frac { p } { 2 } \right) ^ { n }$ converge?
(A) $- 2 < p < 2$ only
(B) $- \frac { 1 } { 2 } < p < \frac { 1 } { 2 }$ only
(C) $\frac { 1 } { 2 } < p < 2$ only
(D) $p < \frac { 1 } { 2 }$ and $p > 2$
(E) There are no such values of $p$.