Find the Interval of Convergence Of $\sum _ { n = 1 } ^ { \infty } \frac { ( x - 2 ) ^ { n } } { n 3 ^ { n } }$

question 235

Multiple Choice

Find the interval of convergence of $\sum _ { n = 1 } ^ { \infty } \frac { ( x - 2 ) ^ { n } } { n 3 ^ { n } }$ .

• A) \(( 1,3 )\)
• B) \([ 1,3 )\)
• C) \(( 2,4 ]\)
• D) \([ 2,4 ]\)
• E) \(( - 1,5 )\)
• F) \([ - 1,5 )\)
• G) \(( - 2,6 ]\)
• H) \(( - \infty , \infty )\)

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Definitions:

Annuity Formula

A mathematical formula used to calculate the future value of an annuity or the payments required to meet a certain future value.

Compound Interest

Interest calculated on the initial principal, which also includes all of the accumulated interest from previous periods.

Exponential Decay

A decrease in quantity that occurs at a rate proportional to the current total, often seen in contexts like radioactive decay.

Arithmetic Operations

Core math processes involving plus, minus, times, and divided by.