- #1
MissP.25_5
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Hello.
How do I find the radius of convergence for this problem?
##\alpha## is a real number that is not 0.
$$f(z)=1+\sum_{n=1}^{\infty}\alpha(\alpha-1)...(\alpha-n+1)\frac{z^n}{n!}$$
I understand that we can use the ratio test to find R. And by using ratio test, I got R=1. But in the answer, it also says that if α is a positive real number, then this series terminates.
==> The radius of convergence is ∞.
I don't understand this part. I hope someone could explain it to me.
How do I find the radius of convergence for this problem?
##\alpha## is a real number that is not 0.
$$f(z)=1+\sum_{n=1}^{\infty}\alpha(\alpha-1)...(\alpha-n+1)\frac{z^n}{n!}$$
I understand that we can use the ratio test to find R. And by using ratio test, I got R=1. But in the answer, it also says that if α is a positive real number, then this series terminates.
==> The radius of convergence is ∞.
I don't understand this part. I hope someone could explain it to me.
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