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Power Series Intervals of Convergence worksheets

Find radii and intervals, test both endpoints separately, and track endpoint changes under termwise operations.

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Find radii and intervals, test both endpoints separately, and track endpoint changes under termwise operations.

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Generated keys distinguish sequence limits, partial sums, infinite-series convergence, endpoint behavior, and approximation error instead of collapsing them into a single answer.

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Determine the radius and verify each endpoint rather than inferring brackets from the radius.

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The governing limit or test, its hypotheses, the calculation, and a precise conclusion.

The worked key preserves the reasoning that distinguishes similar-looking sequence and series tasks.

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  • Have students name the mathematical object before choosing a method.
  • Require separate endpoint checks for power series.
  • Keep exact values and labeled approximations side by side.

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Math SheetNameScoreTeacherDatePower Series Radius and Interval of ConvergenceFind the radius first, then test the left and right endpoints separately. Recheck endpoint behavior after termwise differentiation or integration.1.Use sum_(n=1)^infinity 2/(6^n n^3)(x-0)^n. Find the radius and interval of convergence of the resulting series. Show separate checks at x=-6 andx=6.2.Use sum_(n=1)^infinity 4/(3^n n^1)(x+3)^n. Find the radius and interval of convergence of the resulting series. Show separate checks at x=-6 andx=0.Separate the object, test, endpoint, approximation, and conclusion.math-sheet.comPage 1 of 3
Math SheetNameScoreTeacherDatePower Series Radius and Interval of ConvergenceFind the radius first, then test the left and right endpoints separately. Recheck endpoint behavior after termwise differentiation or integration.3.Integrate sum_(n=1)^infinity 5/(2^n n^1)(x+3)^n term by term with constant C=0 to obtain sum_(n=1)^infinity 5(x+3)^(n+1)/[2^n n^1(n+1)]. Find theradius and interval of convergence of the resulting series. Show separate checks at x=-5 and x=-1.4.Use sum_(n=1)^infinity 4/6^n(x-1)^n. Find the radius and interval of convergence of the resulting series. Show separate checks at x=-5 and x=7.Separate the object, test, endpoint, approximation, and conclusion.math-sheet.comPage 2 of 3
Math SheetNameScoreTeacherDatePower Series Radius and Interval of ConvergenceFind the radius first, then test the left and right endpoints separately. Recheck endpoint behavior after termwise differentiation or integration.5.Differentiate sum_(n=1)^infinity 5/(7^n n^2)(x-2)^n term by term to obtain sum_(n=1)^infinity 5n(x-2)^(n-1)/(7^n n^2). Find the radius and intervalof convergence of the resulting series. Show separate checks at x=-5 and x=9.6.Integrate sum_(n=1)^infinity 4n^1/7^n(x-0)^n term by term with constant C=0 to obtain sum_(n=1)^infinity 4(x-0)^(n+1)/[7^n n^-1(n+1)]. Find theradius and interval of convergence of the resulting series. Show separate checks at x=-7 and x=7.Separate the object, test, endpoint, approximation, and conclusion.math-sheet.comPage 3 of 3

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