Determine the limit of the sequence $a _ { n } = \frac { ( - 2 ) ^ { n } } { n }$ .
A)-2
B)0
C)ln 2
D) $\sqrt { 2 }$
E) $e ^ { 2 }$
F) $- \frac { 1 } { 2 }$
G)1

H)Divergent

Question

Determine the limit of the sequence $a _ { n } = \frac { ( - 2 ) ^ { n } } { n }$ .
A)-2
B)0
C)ln 2
D) $\sqrt { 2 }$ 
E) $e ^ { 2 }$ 
F) $- \frac { 1 } { 2 }$ 
G)1

H)Divergent

Quizplus · Accepted Answer

The sequence $a_n = \frac{(-2)^n}{n}$ does not converge to a finite limit because the numerator $(-2)^n$ oscillates between positive and negative values, causing the sequence to diverge.

Determine the Limit of the Sequence an=(−2)nna _ { n } = \frac { ( - 2 ) ^ { n } } { n }an​=n(−2)n​

Determine the Limit of the Sequence $a _ { n } = \frac { ( - 2 ) ^ { n } } { n }$