The radius of convergence of the power series $\sum _ { n = 1 } ^ { \infty } x ^ { n } / n !$ is
A) 0
B) 1
C) 2
D) $\infty$
E) none of the above

Question

Quizplus · Accepted Answer

The radius of convergence of the power series $\sum _ { n = 1 } ^ { \infty } x ^ { n } / n !$ can be found using the ratio test, which in this case shows that the series converges for all real numbers $x$, indicating an infinite radius of convergence. This series is the expansion of $e^x - 1$, which converges for all $x$.

The Radius of Convergence of the Power Series ∑n=1∞xn/n!\sum _ { n = 1 } ^ { \infty } x ^ { n } / n !∑n=1∞​xn/n!

The Radius of Convergence of the Power Series $\sum _ { n = 1 } ^ { \infty } x ^ { n } / n !$