Question

The series ${\sum }_{n=0}^{\infty }\frac{1}{n!}$ converges to

• A. 2 in 2
• B. $\sqrt{2}$
• C. 2
• D. e

Answer 1

The correct option is D e

$e^x=1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+...$
$Putx=1$
$e=1+1+\frac{1}{2!}+\frac{1}{3!}+...$
$\Rightarrow {\sum }_{n=0}^{\infty }\frac{1}{n!}=e$