Interval of Convergence
Definition
The interval of convergence is the range of x-values for which a power series converges, meaning it approaches a finite value.
Related terms
Radius of Convergence: The radius of convergence is the distance from the center point to the edge of the interval of convergence.
Power Series: A power series is an infinite sum of terms that involve powers (exponents) of a variable.
Convergent Series: A convergent series is a sequence whose partial sums approach a finite limit as more terms are added.
"Interval of Convergence" appears in:
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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