Question

Determine the convergence or divergence of the series ∑ (-1)^(n+1) * n / (n² + 6).

Answer 1

The series ∑ (-1)^(n+1) * n / (n² + 6) converges.

Step-by-step explanation:

To determine the convergence or divergence of the series ∑ (-1)^(n+1) * n / (n² + 6), we can use the Alternating Series Test. This test states that if the terms of an alternating series are decreasing in absolute value and approach zero, then the series converges. In this case, the numerator alternates between positive and negative values, and the denominator increases as n increases, so the terms are decreasing in absolute value. We can also see that the terms approach zero as n approaches infinity. Therefore, the series converges.