Use the integral test to determine if the series is convergent or divergent.

Convergent

Step-by-step explanation:

∑₁°° n / (n² + 1)²

Applying integral test:

∫₁°° x / (x² + 1)² dx

If u = x² + 1, then du = 2x dx, or ½ du = x dx.

When x = 1, u = 2.  When x = ∞, u = ∞.

½ ∫₂°° 1 / u² du

½ (-1 / u) |₂°°

½ (-1 / ∞) − ½ (-1 / 2)

0 + ¼

¼

The integral converges, so the series also converges.

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step-by-step explanation:

the x's and the y's both go up the same amount each time, therefore it will be a linear function because it will go in a straight line when drawn on a graph.

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15 units use socratic

step-by-step explanation: 15 units