Q$7$

Let $f(x)=e$

a$.)$ using the general Taylor series form,

${\displaystyle \underset{n=0}{\overset{}{}}}\frac{f^{(n)}(a)}{n!}(x-a{)}^n$

find the taylor selles representation of $f(x)$ centered at $a=1.$ In your work, show at least $5$ terms of the series before writing the answer in summation notation.

b$.)$ Use the ratio test with your series from part $($a$)$ to find the radius of convergence.