- #1

porroadventum

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**1.**Determine the raius of convergence and interval of convergence of the power series [itex]\sum[/itex] from n=1 to [itex]\infty[/itex] (3+(-1)

^{n})

^{n}x

^{n}.

**2.**Usually when finding the radius of convergence of a power series I start off by using the ratio test: lim

_{n[itex]\rightarrow[/itex]∞}|((3+(-1)

^{n+1})

^{n+1}x

^{n+1}/ (3+(-1)

^{n})

^{n}x

^{n}|

But this limit does not exist since this equation is just oscillating between 0 and +infinity.

Is there a radius of convergence?

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