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

Question

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

Quizplus · Accepted Answer

The sequence $a_n = \frac{(-1)^n}{\sqrt{n}}$ approaches 0 as $n$ goes to infinity. The numerator alternates between -1 and 1, making the sequence oscillate, but the denominator grows without bound, causing the absolute value of each term to get closer and closer to 0.

Determine the Limit of the Sequence an=(−1)nna _ { n } = \frac { ( - 1 ) ^ { n } } { \sqrt { n } }an​=n​(−1)n​

Determine the Limit of the Sequence $a _ { n } = \frac { ( - 1 ) ^ { n } } { \sqrt { n } }$