Determine convergence or divergence of the alternating series.
-$$\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n } \left( \frac { 7 n ^ { 8 } + 3 } { 6 n ^ { 2 } + 7 } \right)$$
A) Diverges
B) Converges

Question

Quizplus · Accepted Answer

The series diverges because the limit of the absolute value of the terms does not approach zero as $ n \to \infty $. Specifically, the dominant term in the numerator is $ 7n^8 $ and in the denominator is $ 6n^2 $, so the terms do not tend to zero.

Determine Convergence or Divergence of the Alternating Series ∑n=1∞(−1)n(7n8+36n2+7)\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n } \left( \frac { 7 n ^ { 8 } + 3 } { 6 n ^ { 2 } + 7 } \right)n=1∑∞​(−1)n(6n2+77n8+3​)

Determine Convergence or Divergence of the Alternating Series $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n } \left( \frac { 7 n ^ { 8 } + 3 } { 6 n ^ { 2 } + 7 } \right)$