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Interval of Convergence

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AP Calculus AB/BC

Definition

The interval of convergence is the range of x-values for which a power series converges, meaning it approaches a finite value.

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Subjects (5)

Practice Questions (9)

Which test can be used to determine the interval of convergence of a power series?
Which of the following statements is true about the interval of convergence of a power series?
If the radius of convergence of a power series centered at 0 is 5, what can be said about the interval of convergence?
What is the interval of convergence of the power series represented by the function f(x) = ∑(n=0 to ∞) (2x)^n/n^2?
If the interval of convergence for a power series is (-4, 6), what can be said about the radius of convergence?
If a power series has a radius of convergence of 0, what can be said about the interval of convergence?
What is the interval of convergence of the power series represented by the function f(x) = ∑(n=1 to ∞) (x-2)^n/n^3?
If the interval of convergence for a power series is (-1, 5), what can be said about the radius of convergence?
Which of the following statements is true regarding the radius and interval of convergence?

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