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

A$.1-\frac{2^2}{2!}+\frac{2^4}{4!}-\frac{2^6}{6!}+$cdots$+\frac{(-1{)}^n{2}^{2n}}{(2n)!}+$cdots$=$

B$.7-\frac{7^3}{3!}+\frac{7^5}{5!}-\frac{7^7}{7!}+$cdots$+\frac{(-1{)}^n{7}^{2n+1}}{(2n+1)!}+$cdots$=$