The function is .

Consider .

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Power series formula: .

Apply integral on each side.

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Substitute in .

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Substitute in .

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Substitute in .

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The power series representation of is .

Find the radius of convergence.

Consider .

Ratio test:

Let be a series with non zero terms.

1. converges absolutely if .

2. diverges if or .

3. The ratio test is inconclusive if .

Here and .

Find .

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The series is converges when .

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Therefore, the radius of the convergence is .

The power series representation of is .

The radius of the convergence is .