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

Question

Quizplus · Accepted Answer

The series diverges because the limit of the terms does not approach zero as $ n \to \infty $. The term $\ln \left[ \frac { 3 n + 7 } { 2 n + 6 } \right]$ approaches $\ln(1.5)$, which is not zero.

Determine Convergence or Divergence of the Alternating Series ∑n=1∞(−1)nln⁡[3n+72n+6]\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n } \ln \left[ \frac { 3 n + 7 } { 2 n + 6 } \right]n=1∑∞​(−1)nln[2n+63n+7​]

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