Interval and radius of convergence Determine

Chapter 8, Problem 19E

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QUESTION:

Interval and radius of convergence Determine the radius of convergence of the following power series. Then test the endpoints to determine the interval of convergence.

\(\sum \frac{k^{20} x^{k}}{(2 k+1) !}\)

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QUESTION:

Interval and radius of convergence Determine the radius of convergence of the following power series. Then test the endpoints to determine the interval of convergence.

\(\sum \frac{k^{20} x^{k}}{(2 k+1) !}\)

ANSWER:

Solution 19E

Step 1:

In this problem we have to determine the radius of convergence of the power series.

Use Root test to determine the radius of convergence.

If and

  1. If L<1, converges.
  2. If L>1, diverges.
  3. If L=1, the test is inconclusive.

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