# How do you find the radius of convergence #Sigma (x^n)/(5^sqrtn)# from #n=[0,oo)#?

The radius of convergence of the series:

is

Let's calculate the ratio:

Now we have:

and as a result:

so that:

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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