Deduce that the power series $\sum _ { n \geqslant 0 } C _ { n } t ^ { n }$ converges uniformly on the interval $I = \left[ - \frac { 1 } { 4 } , \frac { 1 } { 4 } \right]$.
Deduce that the power series $\sum _ { n \geqslant 0 } C _ { n } t ^ { n }$ converges uniformly on the interval $I = \left[ - \frac { 1 } { 4 } , \frac { 1 } { 4 } \right]$.