Radius & Interval of Convergence of Power Series

Define Interval of Convergence

• The range of y-values within which the series will converge

• The range of x-values within which the series will diverge

• The range of x-values within which the series will converge

• The range of y-values within which the series will diverge

Which method would work best for this example?

• Ratio Test

• Geometric

Which method would work best for this example?

• Ratio Test

• Geometric

Why do we test endpoints when determining the interval of convergence?

• Because we like doing extra math.

• The ratio test is inconclusive at these points.

• To make sure all endpoints converge.

• -2 <= x < 4

• -2 < x < 4

• 3 < x < 5

• 3 < x <= 5

• 0 <= x < 8

• 0 < x < 8

• 2 <= x < 6

• 2 < x <= 6

Find the Interval of Convergence and the Radius of Convergence

• IOC: -3<x<1

  ROC: 2

• IOC: -2<x<2

  ROC: 2

• IOC: -3<x<1

  ROC: 1

• IOC: -2<x<2

  ROC: 1

After doing the ratio test, we are left with: |(x-3)/6|. What is the radius if convergence.

• -3

• 9

• 6

• 12