Question

Test the series for convergence or divergence using the Alternating Series Test.

∑ (n=0 to [infinity]) (4 + n^2) sin((n + 1/2)π)

Identify b_n.

Answer 1

To test the series for convergence or divergence using the Alternating Series Test, we need to identify b_n. In this case, the series is given by ∑ (n=0 to ∞) (4 + n^2) sin((n + 1/2)π). To identify b_n, we look at the general term of the series, which is (4 + n^2) sin((n + 1/2)π). From this, we can see that b_n is (4 + n^2).

Step-by-step explanation:

To test the series for convergence or divergence using the Alternating Series Test, we need to identify bn. In this case, the series is given by ∑ (n=0 to ∞) (4 + n2) sin((n + 1/2)π). To identify bn, we look at the general term of the series, which is (4 + n2) sin((n + 1/2)π). From this, we can see that bn is (4 + n2).