Consider the series

${\displaystyle \underset{n=0}{\overset{}{}}}\frac{x^n}{n!}$

a$.$ Find the radius of convergence.

b$.$ Find $S_6(x).$

c$.$ Evaluate the polynomial you found in $($b$)$ at $x=1$

d$.$ Find $\underset{n}{lim}{S}_n(1)$ accurate to $6$ decimal places.

$($Hint: Keep find sums until the $1^{st}$ six decimal places stabilize$)$