Determine whether the sequence defined by $a _ { n } = \frac { 5 ^ { n } } { 8 ^ { n } + 1 }$ converges or diverges. If it converges, find its limit.
A) 1
B) $\frac { 5 } { 8 }$
C) 0
D) Diverges

Question

Quizplus · Accepted Answer

As $ n \to \infty $, the term $ 8^n $ in the denominator grows much faster than $ 5^n $ in the numerator, making the fraction approach 0. Thus, the sequence converges to 0.

Determine Whether the Sequence Defined By an=5n8n+1a _ { n } = \frac { 5 ^ { n } } { 8 ^ { n } + 1 }an​=8n+15n​

Determine Whether the Sequence Defined By $a _ { n } = \frac { 5 ^ { n } } { 8 ^ { n } + 1 }$