Question

$$( \sum _ { n = 1 } ^ { \infty } \frac { 4 ^ { n } } { n ! } )$$

Answer

n=1,-1

Solution


Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[{n}^{2}=1\]
Take the square root of both sides.
\[n=\pm \sqrt{1}\]
Simplify  \(\sqrt{1}\)  to  \(1\).
\[n=\pm 1\]