Question

What conclusions can be made about the series [infinity] 8 cos(πn) n n = 1 and the Integral Test? The Integral Test can be used to determine whether the series is convergent since the function is positive and decreasing on [1, [infinity]). The Integral Test can be used to determine whether the series is convergent since the function is not positive and not decreasing on [1, [infinity]). The Integral Test can be used to determine whether the series is convergent since it does not matter if the function is positive or decreasing on [1, [infinity]). The Integral Test cannot be used to determine whether the series is convergent since the function is not positive and not decreasing on [1, [infinity]). There is not enough information to determine whether or not the Integral Test can be used or not.

Answer 1

Answer:

The conclusions that can be made about the series [infinity] 8 cos(πn) n n = 1 and the Integral Test

IS

The Integral Test can be used to determine whether the series is convergent since it does not matter if the function is positive or decreasing on [1, [infinity])

Step-by-step explanation:

The integral test can be used to test a convergence or divergence of an harmonic series.

If the integral has a definite limit on [1, Infinity], the series is said to CONVERGE. Otherwise, it DIVERGES. It does not matter whether the function is positive on decreasing on [1, Infinity]

If the integral of the function 8 cos(πn) n, over n =[1, Infinity] has a limit, the Integral test will for for its convergence. The function been positive or decreasing on n = [1, Infinity] notwithstanding.