Question

Is the power series∑ n=1[infinity]⁾ᵒ.¹ convergent? If so, what is the radius of convergence?
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Answer 1

The power series ∑ n=1∞ o^n is not convergent and does not have a radius of convergence.

Step-by-step explanation:

The power series ∑ n=1∞ o^n is convergent if the terms approach zero as n approaches infinity. In this case, o^n does not approach zero as n increases, so the power series is not convergent.

The radius of convergence is the distance from the center of the power series to the point at which the series converges. Since this power series does not converge, it does not have a radius of convergence.