Determine the radius of convergence of the power series:

Test for convergence at the boundary points if is finite.

We have

Therefore,

Hence, and the series converges for .

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A Fraction of a Dot
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Determine the radius of convergence of *∑ (1 + 1/n)*^{n2} z^{n}

Determine the radius of convergence of the power series:

Test for convergence at the boundary points if is finite.

We have

Therefore,

Hence, and the series converges for .