Determine whether the given series converges or diverges. If it converges, find its sum. $\sum _ { n = 0 } ^ { \infty } \frac { 9 n ^ { 2 } + 5 } { 2 n ^ { 2 } + 6 }$
A) $\frac { 7 } { 4 }$
B) Diverges
C) $\frac { 9 } { 2 }$
D) $\frac { 5 } { 6 }$

Question

Quizplus · Accepted Answer

The series diverges because the terms do not approach zero as $ n \to \infty $. The limit of the terms is $\frac{9}{2}$, which is not zero, indicating divergence.

Determine Whether the Given Series Converges or Diverges ∑n=0∞9n2+52n2+6\sum _ { n = 0 } ^ { \infty } \frac { 9 n ^ { 2 } + 5 } { 2 n ^ { 2 } + 6 }∑n=0∞​2n2+69n2+5​

Determine Whether the Given Series Converges or Diverges $\sum _ { n = 0 } ^ { \infty } \frac { 9 n ^ { 2 } + 5 } { 2 n ^ { 2 } + 6 }$