By recognizing each series below as a Taylor series evaluated at a particular value of $x$, find the sum of each convergent series.

A. $1 + {1\over 3} + ({1\over 3})^2 + ({1\over 3})^3 + ({1\over 3})^4 + \cdots + ({1\over 3})^n + \cdots =$

B. $1 + 3 + {3^2\over 2!} + {3^3\over 3!} + {3^4\over 4!} + \cdots + {3^n\over n!} + \cdots =$