Find the Radius of Convergence and the Interval of Convergence $$\sum _ { n = 0 } ^ { \infty } \frac { ( 7 x ) ^ { n } } { n ! }$$

question 58

Multiple Choice

Find the radius of convergence and the interval of convergence of the power series. $$\sum _ { n = 0 } ^ { \infty } \frac { ( 7 x ) ^ { n } } { n ! }$$

• A) \(R = 7 , I = ( - 7,7 )\)
• B) \(R = 0 , I = \{ 0 \}\)
• C) \(R = 7 , I = [ - 7,7 ]\)
• D) \(R = \infty , I = ( - \infty , \infty )\)

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Definitions:

Continuous Random Variables

Continuous random variables are quantities that can assume an infinite number of values within a given range, often corresponding to measurements.

Normal Distributions

A distribution where the likelihood of data occurring decreases as the distance from the mean increases, all the while maintaining a symmetrical shape around the mean.

Discrete Random Variable

A random variable that can take on only a finite or countably infinite set of distinct values.

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