Long description: workbook16block4fig1

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A number line illustrating the interval of convergence for a power series, marked with symbols indicating convergence and divergence.

Alt text: A number line illustrating the interval of convergence for a power series, marked with symbols indicating convergence and divergence.

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  • The image displays a horizontal number line with an arrow indicating the positive direction along the x-axis.
  • Points labeled \text{-R}, 0, and \text{R} are marked on the number line, suggesting interval boundaries.
  • The region extending to the left of \text{-R} and the region extending to the right of \text{R} are labeled with a wavy line and the word "divergent", indicating that the power series diverges outside the interval \text{(-R, R)}.
  • The segment between \text{-R} and \text{R} is marked with a filled gray line and labeled "convergent", indicating that the power series converges within the interval \text{[-R, R]}.
  • The symbols on the number line, specifically at \text{-R} and \text{R}, suggest the endpoints might be included in the interval of convergence, although the labeling focuses on the interval itself.

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