Identify the Interval of Convergence of a Power Series $\sum _ { n = 1 } ^ { \infty } n ( 2 x ) ^ { n }$

question 30

Multiple Choice

Identify the interval of convergence of a power series $\sum _ { n = 1 } ^ { \infty } n ( 2 x ) ^ { n }$

• A) \(- \frac { 1 } { 2 } < x < 0\)
• B) \(- \frac { 1 } { 2 } < x < \frac { 1 } { 2 }\)
• C) \(0 < x < \frac { 1 } { 2 }\)
• D) \(- \frac { 1 } { 4 } < x < \frac { 1 } { 4 }\)
• E) \(0 < x < \frac { 1 } { 4 }\)

---

Definitions:

Fraction

A mathematical expression representing the division of one whole number by another, not resulting in a whole number.

Roman Numeral

A numeral system originating in ancient Rome, using combinations of letters from the Latin alphabet (I, V, X, L, C, D, M) to signify values.

Whole Number

A numerical value without fractions or decimals, often used to count discrete objects.

Fraction

A mathematical expression representing the division of one integer by another, typically used to denote a part of a whole.