Question

Find the coefficient of $x$ in the expansion of $(1+\frac{x}{1!}+\frac{x^2}{2!}+\frac{x^3}{3!}+...+\frac{x^n}{n!})$

Answer 1

$1+\frac{x}{1!}+\frac{x^2}{2!}+\frac{x^3}{3!}+.....+\frac{x^n}{n!}$

Therefore,

Coefficient of $x=\frac{1}{1!}=\frac{1}{1}=1$

Hence the coefficient of $x$ in the given expression is $1$.